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Arithmetic of automorphic forms of many variable : reconstruction of the foundation

Research Project

Project/Area Number 09440007
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionThe University of Tokyo

Principal Investigator

ODA Takayuki  Professor, the Graduate School of Math. Sci., the Uni. of Tokyo, 大学院・数理科学研究科, 教授 (10109415)

Co-Investigator(Kenkyū-buntansha) SAITO Hiroshi  Prof. Grad. School of Hum. & Env. Studies, Kyoto Univ., 大学院・人間環境学研究科, 教授 (20025464)
IBUKIYAMA Tomoyoshi  Prof. Grad. Sch. of Sci., Osaka Univ., 大学院・理学研究科, 教授 (60011722)
ARAKAWA Tsuno  Prof. Faculty of Science, St. Paul Univ., 理学部, 教授 (60097219)
HIRONAKA Yumiko  Prof. Fac. of Edu., Waseda Univ., 教育学部, 教授 (10153652)
TAKASE Kouichi  ASS. Prof. Fac. of Edu., Miyagi Edu. Univ., 教育学部, 助教授 (60197093)
山崎 正  神戸大学, 理学部, 教授 (30011696)
菅野 孝史  金沢大学, 理学部, 教授 (30183841)
村瀬 篤  京都産業大学, 理学部, 教授 (40157772)
Project Period (FY) 1997 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥10,900,000 (Direct Cost: ¥10,900,000)
Fiscal Year 1999: ¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1998: ¥4,400,000 (Direct Cost: ¥4,400,000)
Fiscal Year 1997: ¥3,600,000 (Direct Cost: ¥3,600,000)
KeywordsAutomorphic forms / L-functions / Spherical functions / Modular forms / Special functions / L関数 / L-関数
Research Abstract

As planned in our application, at Tokyo and at Kobe we had a series of monthly seminars. Since we have already reported about them in the annual reports, here we do not write about them. We also omit the details about the workshops at RIMS, Kyoto University and the summer schools. The proceedings on these meetings are available. The head investigator Oda in a joint work with Takahiro HAYATA (Yamagata Univ.) and Harutaka KOSEKI (Mie University) obtained an explicit formula for matrix coefficients of the middle discrete series of SU(2,2). Added to this he also obtained explicit formulae of matrix coefficients for the large discrete series of SU(2,2) and Sp(2,R). Moreover in a joint paper with Masao TSUZUKI (Sophia Univ.) he constructed Green functions of modular divisors on arithmetic quotients of certain bounded symmetric domains, as automorphic forms. We also explain the outline of the fruits of the research by the investigators joined to this plan. This result has not only have applic … More ations for the dimension of spaces of automorphic forms, but also theoretically significance. Ibukiyama and Saito had remarkable results on the evaluation of the special values of the zeta functions of prehomogeneous vector spaces. This result has not only application to the explicit dimension formulae of the spaces of automorphic forms, but also theoretically very important meaning. The investigation of p-adic spherical functions by Sato and Hironaka made much progress. The new point among others is that they can handle also the case of "ramified" spherical functions. The joint work of Murase and Sugano also advanced. Their work of the primitive theta function of SU(2,1) is one interesting result. But also the is a progress in the theory of automorphic L-functions on orthogonal groups A joint work with Shin-ichi Kato (Kyoto Univ.) on p-adic spherical functions is one of fruits. Watanabe together with Masanori Morishita (Kanazawa Univ.) pushed forward the investigation of Hermite constants for algebraic groups, Which is so to speak a non-abelian version of "Geometry of Numbers". The result of Katsurada is also interesting by regarding it as an investigation of ramified p-adic spherical functions. Less

Report

(4 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report
  • Research Products

    (157 results)

All Other

All Publications (157 results)

  • [Publications] Takahiro HAYATA: "Matrix coeffiaciente of the principal Pj-series and the middle discrete serious of SO(2,2)"Advanced Stadies in pare in athemetics. 26. 49-75 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Toshiyuki KOBAYASHI: "A varciding theorem for modular symlbal on tocally suymantsis syaces"Commentarii Math. Helvetia. 73. 45-70 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takahiro HAYATA: "An expidiat integral nepresentition of whith aber functions for the reprefemtation of the discrete serses the case of SO(2,2)"J. of Math, Kyoto University. 37. 519-530 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takuya MIYAZAKI: "Principal Series Whittaker functious on SO(Li IR), II"Tohoku Math. J.. 50. 243-260 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 織田孝幸: "保型形式の数論のための実解析"数学(日本数学会,岩波書店). 350-357 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tsuneo ARAKAWA: "A note on the siestuictions rap for Jacotiforu\ms"Abh. Math. Sem. Univ. Hamburg. 69. 309-317 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tsuneo ARAKAWA: "On Poly-Bernooulli numbers"Commentaris Math. Univ. St. Pauli. 48. 159-167 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tsuneo ARAKAWA: "Multipeta valuses, plly-Bernoulli nunleis, and nobated beta functions"Nagoya Math. J. 153. 187-209 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tsuneo ARAKAWA: "Kocher-MaaB Dirichlet series corresponding to Jacolil fornes and coher Eisenstain seies"Commentarii Math. Univ. St. Paul. 47. 93-122 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tomoyashi IBUKIYAMA: "On squared Mobius function for haffintegral niatries and it application"J. of Number Theory.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tomoyoshi IBUKIYAMA: "On differential operators on autornorphic forms and invariant phurihitmouic polynomials"Commentarii Math. Univ. St. Paul.. 48. 103-118 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tomoyoshi IBUKIYAMA: "On some elementary character sums"Commentarii Math. Univ. St. Paul.. 47. 7-13 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] W. Eholzer: "Rankin-Coken type differential operators for singal modul for us"International J. Math. 9-4. 443-463 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tomoyoshi IBUKIYAMA: "On the roaded ning of modular forms of the singal paramodul group of level 2"Abh. Math. Sem. Univ. Hamburg. 67. 297-305 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tomoyoshi IBUKIYAMA: "On geta dunctions associated to Symmetric matisces III. An orhicif form of L-functions"Nagoya Math. J. 146. 149-188 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 伊吹山知義: "「やさしい」ゼータ関数について"数学(日本数学会,岩波書店). 50-1. 1-11 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masao KOIKE: "Hypergeonitisc polynomials orer finite fiokdo"Tohoku Math. J.. 51. 75-79 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Maso KOIKE: "A note on hypergeoutisc polynomials ones finist field"Advanced studies in comtemporous Math. (Algobmie Number Theory) in Memoius of the Janjun Math. 1. 35-43 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidenori KATSURADA: "Square Mobius function for half-integal inatrious"Contemporary Math.. 249. 235-248 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidenori KATSURADA: "A short proof of Kitaoka-Feit induction lemma fun Singal series"Abh. Math. Sem. Univ. Hamburg. 68. 297-304 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidenori KATSURADA: "A power series attached to local deusitias of forms of higher clegred"Hong Kong Math. J. 2. 297-304 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidenon KATSURADA: "An explicat formula for siegal series"Amer. J. Math. 121. 415-452 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidemori KATSURADA: "A necursion formula for local densities with conruence condition"Mem. Muroyan Inrt. Tech. 47. 97-102 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidemori KATSURADA: "A ricuision formula for local densities of quaohatis forms"J. Namber Theory. 64. 183-210 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidemori KATSURADA: "A remark on Kitaoka formal power series utlached to local deusity"Manuocripta Math.. 92. 477-486 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidemori KATSURADA: "An explicit formula for the Fousier coofficients of Siogel-Eiseustain series of deyer3"Nagoya Math. J. 146. 199-223 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hiroshi SAITO: "Explicit form of the peta fomchoris of pre homogeneous vector snaces"Math. Annaliu.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hiroshi SAITO: "Explicit formula of orhital p-adic geta functions associatial to simmetisc and hermitian matrices"Commentarii Math. Univ. Santa Pauli. 46. 175-216 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Fumihiro SATO: "Local deusities of sepresentations of quadiatis forms over p-adic integeou : the non-dyadic case"J. fo Number Theory.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Fumihiro SATO: "6-Functions of prehomogeneous rector snaces attached to play mauifoldo of the general linear grous"Commentarii Math. Univ. St. Pauli. 48. 129-136 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Fumihiro SATO: "Eisenstein series on weakly spherical homogeneous suaccs of GL(n)"Tshoku Math. J. 50. 23-69 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Atsushi MURASE: "Local theory of primiture theta functions"Compritio Math.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Atsushi MURASE: "On standard L-functions attached to autca orphic forms on definite orthogoral groups"Nagoya Math. J. 152. 57-96 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Ki-ichiro HASHIMOTO: "Q-curves of deysee 5 and jacobian surfaces of GL<@D22@>D2-type"manuscripta math.. 98. 165-182 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Ki-ichiro HASHIMOTO: "On the Sato-Tate conjunture for QM-curues of gerius two"Mathewatico of Computation. 68-228. 1649-1662 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yumiko HIRONAKA: "Local deusities of hesmitian formis"Contemporary Math. (Integral Quadratic Forums and Lattices). 249. 135-148 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yumiko HIRONAKA: "Spherical function and local densities on hermition forms"Jounal of Math. Soc. Japan. 51. 553-581 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yumiko HIRONAKA: "Local geta functions on hermitiou frms and its application to local deudity"Journal of Numla Theory. 71. 40-64 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masanori MORISHITA: "Adele gcometry of numleis"Advanced Studies in pure math.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takao WATANABE: "Acompasison of automorphic L-functions in a theta series tfting of unitary groups"Israel J. of Math.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takao WATANABE: "Upper tounds of Hermite constants for orthogonal groups"Consnientarii Math. Univ. Sanoti Pauli. 48. 25-33 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 菅野孝史(編): "数理解析研究所講究録1052 "保型形式と整数論""京都大学数理解析研究所. 230 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 都築正男(編): "数理解析研究所講究録1094 "Sp(2,IR)とSU(2,2)上の保型形式II""京都大学数理解析研究所. 117 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 水元信一郎(編): "数理解析研究所講究録1103 "保型形式とL関数の研究""京都大学数理解析研究所. 199 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 村瀬篤,広中由美子(編): "整数論サマースクール報告集(第5回)"Siegel保型形式入門""218 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 橋本喜一郎,百瀬文之(編): "第6回整数論サマースクール報告集「楕円曲線とそのArithmetic Module」"205 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 渡部隆夫(編): "第7回整数論サマースクール報告集「代数群の整数論入門」"279 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takahiro HAYATA, Takayuki ODA: "An explicit integral representation of Whittaker functions for the representations of the discrete series - the case of SU(2,2)-"Journal of Math., Kyoto University. vol. 37. 519-530 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takuya MIYAZAKI. Takayuki ODA: "Principal series Whittaker functions on Sp(2;R), II"Tohoku Math J.//. vol. 50. 243-260 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Toshiyuki KOBAYASHI, Takayuki ODA: "A vanishing theorem for modular symbols on locally symmetric spaces"Commentarii Math. Helvetici. vol. 73. 45-70 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takayuki ODA: "Real Analysis for Arithmetic of Automorphic Forms (In Japanese), Sugaku"Japan Math. Soc.. vol. 50-No. 4. 350-357 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takahiro HAYATA, Harutaka KOSEKI. Takayuki ODA: "Matrix coefficients of the principal P_J-series and the middle discrete series of SU(2,2)"Advanced Studies in pure Math., "Analysis on Homogeneous Spaces and Representation Theory of Lie Groups. vol. 26. 49-75 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tsuneo ARAKAWA: "Koecher-Maass Dirichlet series corresponding to Jacobi forms and Cohen Eisenstein series"Commentarii Math. Univ. St. Pauli. vol. 47. 93-122 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tsuneo ARAKAWA, Masanobu KANEKO: "Multiple zeta-values, poly-Bernoulli numbers and related zeta functions"Nagoya Math. J.. vol 153. 189-209 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tsuneo ARAKAWA, Masanobu KANEKO: "On poly-Bernoulli numbers"Commentarii Math. Univ. St. Pauli. vol. 48. 159-167 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tsuneo ARAKAWA: "Siegfried Boecherer, A note on the restriction map for Jacobi forms"Abh. Math. Sem. Univ. Hamburg. vol. 69. 309-317 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tomoyoshi IBUKIYAMA, Hiroshi SAITO: "On zeta functions associates to symmetric matrices III"An explicit form of L-functions, Nagoya Math. J.. vol. 146. 149-183 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tomoyoshi IBUKIYAMA: "On the graded ring of modular forms of the Siegel paramodular group of level 2"Abh. Math. Sem. Univ. Hamburg. vol. 67. 297-305 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tomoyoshi IBUKIYAMA: "On some elementary character sums"Commentarii Math. Univ. St. Pauli. vol. 47. 7-13 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tomoyoshi IBUKIYAMA, Hiroshi SAITO: "On "elemetary" zeta functions (in Japanese)"Sugaku, Japan Math. Soc.. Vol. 50-No. 1. 1-11 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Wolfgang Eholzer, Tomoyoshi IBUKIYMA: "Rankin-Cohen type differential operators for Siegel modular forms"Internat. J. of Math.. vol. 9. 443-463 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tomoyoshi IBUKIYAMA: "On differential operators on automorphic forms and invariant pluri-harmonic polynomials"Commentarii Math. Univ. St. Pauli. vol. 48. 103-118 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidenori KATSURADA: "Square Moebius function for half-integral matrices"Contemporary Math.. vol. 249. 235-248 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidenori KATSURADA: "A short proof of Kitaoka-Feit induction lemma for Siegel series"Abh. Math. Sem. Hamburg. vol. 68. 297-304 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidenori KATSURADA: "A power series associated with local densities of forms of higher degrees."Bull Hong Kong Math. Soc. 2. no. 2. 297-304 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidenori KATSURADA: "An explicit formula for Siegel series. Amer. J. Math."121, no. 2. 415-452 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidenori KATSURADA, Masaki HISASUE: "A recursion formula of local densities with congruence conditions."Mem. Muroran Inst. Technol.. No. 47. 97-102 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidenori KATSURADA, Masaki HISASUE: "A recursion formula for local densities of quadratic forms."J. Number Theory. 64, no. 2. 183-210 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidenori KATSURADA: "A remark on Kitaoka formal power series attached to local densities"Manuscripta Math.. 92, no. 4. 477-486 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hidenori KATSURADA: "An explicit formula for the Fourier coefficients of Siegel-Eisenstein series of degree $3$"Nagoya Math. J.. 146. 199-223 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masao KOIKE: "Special functions over finite fields"Three Lectures in Algebra, Lecture Note Series No. 41 of Sophia University at Tokyo. 1-24 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masao KOIKE: "Hypergeometric polynomials over finite fields"Tohoku Math. J.. 51. 75-79 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masao KOIKE: "A note on hypergeometric polynomials over finite field"Advanced studies in Contemporary Math. Algebraic Number Theory. 1. 35-43 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masao KOIKE: "Binary, ternary, quaternary codes and modular forms with respect to non-compact triangle arithmetic Fuchsian groups"Workshop on algebraic geometry "Moduli of Varieties and Representations", Hokkaido Univ., January. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Fumihiro SAT0: "b-Functions of prehomogeneous vector spaces attached to flag manifolds of the general linear group"Commentarii Math. Univ. St. Paul.. vol. 48. 129-136 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Fumihiro SAT0: "Eisenstein series on weakly spherical homogeneous spaces of GL(n)"Tohoku Math. J.. vol. 50. 23-69 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Fumihiro SAT0, Yumiko HIRONAKA: "Local densities of representations of quadratic forms over p-adic integers (the non-dyadic case)"Journal of Number Theory. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hiroshi SAITO: "Explicit formula of orbital p-adic zeta functions associated to symmetric and hermitian matrices"Commentarii Math. Univ. St. Pauli. vol. 46. 175-216 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tomoyoshi IBUKIYAMA, Hiroshi SAITO: "On zeta functions assocaites to symmetric matrices III"An explicit form of L-functions, Nagoya Math. J.. vol. 146. 149-183 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hiroshi SAITO: "Explicit form of the zeta functions of piehomogeneous vector spaces"Math. Annalen. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Atsushi MURASE, Takashi SUGANO: "On standard L-functions attached to automorphic forms on definite orthogonal groups"Nagoya Math. J.. 152. 57-96 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Atsushi MURASE, Takashi SUGANO: "Local theory of primitive theta functions"Composition Math.. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Kouichi TAKASE: "On Siegel modular forms of half-integral weights and Jacobi forms"Trans. Amer. Math. Soc.. vol. 351. 735-780 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Kiichiro HASHIMOTO: "Q-curves of degree 5 and jacobian surfaces of GL_2-type"Manuscripta math.. 98. 165-182 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Kiichiro HASHIMOTO, Hiroshi TSUNOGAI: "On Sato-Tate conjecture for QM-curves of genus two"Math. of Computation. vol. 68. 1649-1662 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Kiichiro HASHIMOTO, Katsuya MIYAKE: "Inverse Galois problem for dihedral groups"Number Theory and Its Applications. 165-181 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yumiko HIRONAKA: "Local zeta functions on Hermitian forms and its application to local densities"J. Number Theory. 71, no. 1. 40-64 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yumiko HIRONAKA: "Yumiko Spherical functions and local densities on Hermitian forms."J. Math. Soc. Japan. 51, no. 3. 553-581 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yumiko HIRONAKA: "Local densities of hermitian forms, in Integral Quadratic Forms and Lattices"Contemporary, Math.. vol. 249. 135-148 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takao WATANABE: "Some elementary properties of Hardy-Littlewood homogeneous spaces"Commentarii Math. Univ. St. Pauli. vol. 46. 3-14 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masaki MORISHITA, Takao WATANABE: "S-Hardy-Littlewood homogeneous spaces"International J. of Math.. vol. 9. 732-757 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takao WATANABE: "Upper bound of Hermite constants for orthogonal groups"Commentarii Math. Univ. St. Pauli. vol. 48. 25-33 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takao WATANABE: "On an analog of Hermite's constant"J. of Lie Theory. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takao WATANABE: "A comparison of automorphic L-functions in a theta series lifting of unitary groups"Israel J. Math.. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masaki MORISHITA, Takao WATANABE: "Adele geometry of numbers"Advanced Studies in pure Math.. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takashi SUGANO: "Kokyu-Roku No. 1052 "Automorphic Forms and Number Theory""RIMS, Kyoto Univ.. 230 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masao TSUZUKI: "Kokyu-Roku No. 1094 "Automorphic Forms on Sp (2;R) and SU(2,2)""RIMS, Kyoto Univ.. 117 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shin-ichiro MIZUMOTO: "Kokyu-Roku No. 1103 "Automorphic Forms and L-functions""RIMS, Kyoto Univ.. 199 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Atsushi MURASE and Yumiko HIRONAKA: "Proceeding of Summer School on Number Theory No. 5 "Introduction to Siegel modular forms""218 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Kiichiro HASHIMOT0: "Proceeding of Sumer School on Number Theory No. 6 "Elliptic curves and their arithmetic moduli""205 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takao WATANABE: "Proceedings of Summer School on Number Theory No. 7 "Introduction to arithmetic of algebraic groups""279 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takahiro HAYATA: "Matrix coefficients of the principal P_j - series and the middle deiscrete series of SU(2.2)"Advanced Studies in pure mathematics. 26. 49-75 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Toshiyuki KOBAYASHI: "A vanishing theorem for modular symbols on locally symmetric spaces"Commentarii Math Helvetia. 73. 45-70 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Takahiro HAYATA: "An explicit integral representation of whittaker funchons for the representations of the discrete series -the case of SU(2.2)"J. of Math., Kyoto University. 37. 519-530 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] Takuya MIYAZAKI: "Principal series whittaker functions on Sp(2;IR),II"Tohoku Math. J.. 50. 243-260 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] 織田 孝幸: "保型形式の数論のための実解析"数学(日本数学会、岩波書店). 50-4. 350-357 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Tsuneo ARAKAWA: "A note on the restriction map for Jacobi forms"Abh. Math. Sem. Univ. Hamburg. 69. 309-317 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Tsuneo ARAKAWA: "On Poly-Bernoulli numbers"Commentarii Math.. Univ. St. Pauli. 48. 159-167 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Tsuneo ARAKAWA: "Multiple zeta valumes Poty-Bernoulii numbers, and related zeta functions"Nagoya Math. J. 153. 189-209 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Tsuneo ARAKAWA: "Kocher-MaaB Dirichlet series corresponding to Jacobi forms and cohen Eisenstein series"Commentarii Math. Univ. St. Pauli. 47. 93-122 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Tomoyoshi IBUKIYAMA: "On squared Mobius function for half integral matrices and its application"J. of Number Theory. (印刷中).

    • Related Report
      1999 Annual Research Report
  • [Publications] Tomoyoshi IBUKIYAMA: "On differential operators on automorphic forms and invariant pluriharmonic polynomials"Commertarii Math. Univ. St. Pauli. 48. 103-118 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Tomoyoshi IBUKIYAMA: "On some elementaly character sums"Commentarii Math. Univ. St. Pauli. 47. 7-13 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] W. Eholzer: "Rankin-Cohen type differential operators for Siegel modular forms"International J. Math.. 9-4. 443-463 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Tomoyoshi IBUKIYAMA: "On the graded ring of modular forms of the Siegel paramodular gronp of level 2"Abh. Math. Sem. Univ. Hamburg. 67. 297-305 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] Tomoyoshi IBUKIYAMA: "On zeta functions associated to symmetric matrices III. An explicit form of L-functions."Nagoya Math. J. 146. 149-183 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] 伊吹山 知義: "「やさしい」ゼータ関数について"数学(日本数学会、岩波書店). 50-1. 1-11 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Masao KOIKE: "Hypergeometric polynomials over finite fields"Tohoku Math. J.. 51. 75-79 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Masao KOIKE: "A note on hypergeometric polymomials over finite field"Advanced studies in contemporary Math. (Algebraic Number Theory) in Memoirs of the Janjun Math. Soc.. 1. 35-43 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Masao KOIKE: "Special Functions over Finite Fields"上智大学数学講究録講究録No.41 Threr Lectures in Algebra. 1-24 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Hidenori KATSURADA: "Square Mobius function for half-integral matrices"Contemporary Math.. 249. 235-248 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Hidenori KATSURADA: "A short proof of Kitaoka-Feit induction lemma for Siegel series"Abh. Math. Sem. Hamburg. 68. 297-304 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Hidenori KATSURADA: "A power series attached to local densities of forms of higher degree"Hong Kong Math. J.. 2. 297-304 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Hidenori KATSURADA: "An explicit formula for Siegel series"Amer. J. Math.. 121. 415-452 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Hidenori KATSURADA: "A recursion formula for local densities with congruence conditions"Mem. Muroran Inrt. Tech.. 47. 97-102 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] Hidenori KATSURADA: "A recursion formula for local densities of quachatic forms"J. Number Theory. 64. 183-210 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] Hidenori KATSURADA: "A remark on Kitaoka formal power series attached to local density"Manuscripta Math.. 92. 477-486 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] Hidenori KATSURADA: "An explicit formula for the Fourier coefficients of Siegel-Eisenctein series of degree 3"Nagoya Math.. J.. 146. 199-223 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] Hiroshi SAITO: "Explicit form of the zeta functions of prehogeneous vector spaces"Math. Annal.. (印刷中).

    • Related Report
      1999 Annual Research Report
  • [Publications] Hiroshi SAITO: "Explicit formula of orbital p-adic zeta functions associated to symmetric and hermitian matrices"Commentarii Math. Univ. Santi Pauli. 46. 175-216 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] Fumihiro SATO: "Local densities of representations of quadratic foums over p-adic integers : the non-dyadic case"J. of Number Theory. (印刷中).

    • Related Report
      1999 Annual Research Report
  • [Publications] Fumihiro SATO: "b-Functions of prehomogeneous vector spaces attached to flag manifoldo of the general linear gronp"Comentarii Math. Univ. St. Pauli. 48. 129-136 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Fumihiro SATO: "Eisenstein series on weakly spherical homogeneous spaces of GL(n)"Tohoku Math. J.. 50. 23-69 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Atushi MURASE: "Local theory of primitive theta functions"Compositio Math.. (印刷中).

    • Related Report
      1999 Annual Research Report
  • [Publications] Atushi MURASE: "On standard L-functions attached to automorphic forms on definite orthogoral groups"Nagoya Math. J.. 152. 57-96 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Ki-ichiro HASHIMOTO: "Q-curves of degree 5 and jacobian surfaces of GL_2-type"Manuscripta Math.. 98. 165-182 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Ki-ichiro HASHIMOTO: "On the Sato-Tate conjecture for QM-curves of genus two"Mathematics of Computation. 68-228. 1649-1662 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Yumiko HIRONAKA: "Local densities of hermition forms"Contemporary Math. (Integral Quadratic Forms and Lattices). 249. 135-148 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Yumiko HIRONAKA: "Spherical function and local densities on hermition forms"Journal of Math. Soc. Japan. 51. 553-581 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Yumiko HIRONAKA: "Local zeta functions on hermition forms and its application to local density"Journal of Number Theory. 71. 40-64 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Masanori MORISHITA: "Adele geometry of numbers"Advanced Studies in pure math.. (印刷中).

    • Related Report
      1999 Annual Research Report
  • [Publications] Takao WATANABE: "A comparison of automorphic L-functions in a theta series lifting of unitary groups"Israel J. of Math.. (印刷中).

    • Related Report
      1999 Annual Research Report
  • [Publications] Takao WATANABE: "Upper bounds of Hermite constants for orthogonal groups"Commentarii Math. Univ. Sanoti Pauli. 48. 25-33 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 菅野孝史(編集者): "数理解析研究所講究録1052"保型形式と整数論""京都大学数理解析研究所. 230 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 都築 正男(編集者): "数理解析研究所講究録1094"Sp(2;1R)とSU(2,2)上の保型形式II""京都大学数理解析研究所. 117 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 水本 信一郎(編): "数理解析研究所講究録1103"保型形式とL関数の研究""京都大学数理解析研究所. 199 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 村瀬篤・広中由美子(編): "整数論サマースクール報告集(第5回)"Siegel保型形式入門""218 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] 橋本喜一郎・百瀬文之(編): "第6回整数論サマースクール報告集「楕円曲線とそのArithmetic moduli」"205 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 早田孝博、古関春隆、織田孝幸: "Matrix coefficients of the pricipal P_J-series and the middle discrete series of SV(2,2)" Advanced Studies in pure mathematics. (印刷中). 27 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 織田孝幸: "保型形式の数論のための実解析" 数学. 50-4. 350-357 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 荒川 恒男: "Koecher-MaaB-Dirichlet series corresponding to Jucobi forming and Cohen Eisenstein series" Commentarii math.Univ.St.Pauli. 47. 93-122 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 小池 正夫: "Hypergeometric plynomials over finite fields" Tohoku Math.J.51. 75-79 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 佐藤 文広: "Eisenstein series on weakly spherical homogeneous succes of GL(n)" Tohoku Math.J.50. 23-69 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 村瀬篤、菅野孝史: "On standard L-functions attached to antomophic forms on definite othogival glones" Nagoy math.J.152. 1-40 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 早田孝博・織田孝幸: "An epplicit integral representation of Whittaker functions for the representations of the disciete seias-the case of SU(2,2)-" Journal of Mathemztico,Kyoto University. 37-3. 519-530 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 小林俊行・織田孝幸: "A vaniching theorem for modular symbols on locally symmetric spaces" Commen.Math.Helvetici. (印刷中).

    • Related Report
      1997 Annual Research Report
  • [Publications] "第5回整数論サマースクール報告集「Siegal保型形式入門」" 簡易製本による報告集(村瀬篤・広中由美子編集), 218 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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