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Investigation of Eisenstein series on bounded symmeric domain

Research Project

Project/Area Number 09640002
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionMuroran Institut of Technology

Principal Investigator

KATSURADA Hidenori  Muroran Institute of Technology, Professor, 工学部, 教授 (80133792)

Co-Investigator(Kenkyū-buntansha) CHIGIRA Naoki  Muroran Institute of Technology, Associate Professor, 工学部, 助教授 (40292073)
SATO Motohiko  Muroran Institute of Technology, Associate Professor, 工学部, 助教授 (30254139)
TAKEGAHARA Yugen  Muroran Institute of Technology, Associate Professor, 工学部, 助教授 (10211351)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 1998: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1997: ¥1,900,000 (Direct Cost: ¥1,900,000)
KeywordsEisenstein series / Siegel series / Fourier coefficients / Maass zeta function / Squared Moebius function / Local density / アイゼンシユタイン級数 / マ-スゼータ関数
Research Abstract

1. We gave an explicit formula for the Siegel series on any local field (partly with T.Watanabe). As a result, we gave an explicit formula for the Fourier coefficient of the Siegel-Eisenstein series. In particular, we made a table of Fourier coefficients of Siegel-Bisenstein series of degree 3 (with S.Sugawara).
2. Using the result of 1 we determined a 'good' Euler factor of a zeta function of Andrianov type for the Siegel- Eisenstein series.
3 We gave a simpler proof to the induction formula for Siegel series by Y.Kitaoka and P.Feit.
4. On the set of integral quadratic forms, we defined an analogue of the square of the usual Moebius function, which we call squared Moebius function.
5. We related the Kocher-Maass zeta function for a Siegel modular form in terms of the standard zeta function for it and the squared Moebius function. As a result, we gave an explicit form of the Maass zeta function for the Klingen-Eisenstein lift of a cusp form of one variable (with T.Ibukiyama), This result has been generalized to some extent. Besides, we gave a remarkable result on the vanishing of the Maass zeta function.
6. Using the squared Moebius function, we gave a simpler proof to a result of T.Ibukiyama and H.Saito on an explicit form of the zeta function for symmetric matrices.
7. We gave a precise result on the demominator of a certain power series associated with local densities of quadratic forms.

Report

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

    (56 results)

All Other

All Publications (56 results)

  • [Publications] Hidenori Katsurada: "A recursion formula for local densities" Journal of Number Theory. 64. 183-210 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hidenori Katsurada: "A remark on Kitaoka formal power series attached to local densities" Manuscripta Mathematica. 92. 477-486 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hidenori Katsurada: "An explicit formula for the Fourier coefficients of Siegel Eisenstein series of degree 3" Nagoya Mathematical Journal. 146. 199-223 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hidenori Katsurada: "A recursion formula of local densities with congruence conditions" 室蘭工業大学紀要. 47. 97-102 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hidenori Katsurada: "An explicit formula for the Fourier coefficients of Siegel Eisemstein series" 数理解析研究所 講究録. 1002. 55-69 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hidenori Katsurada: "A Square Moebius function over quadratic forms and its applications to Siegel modular forms" Proc.of 5-th International Conference on Finite or Infinite Dimensional Complex Analysis. 151-155 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "A short proof of Kitaoka-Feit Induction lemma for Siegel series" Abhandlungen aus dem Mathematishen Semiror der Universifat Hamburg. 68. 297-304 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "A Power series associated with local densities of forms of higher degree" Bulletin of the Hong Kong Mathematical Society. 2. (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "An explicit formula for Siegel series" American Journal of Mathematics. 121. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 伊吹山知義: "Koecher-Maass Dirichtet series for Eisensfein series of Klingen type" 数理解析研究所講究録. 965. 41-51 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 桂田英典: "An integral expression of Koecher-Maass Dirichlet series and its applications (after T-Arahur)" 第1回整数論オータムワークショップ報告集. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "Squared Mobius function for half-integral matrices" Contemporary Math.(1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 竹ヶ原 裕元: "On the number of crossed homomorphisms from a finite cyclic p-group to a finite p-group" 数理解析研究所講究録. 1057. 38-40 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] G.Chen: "Finite groups with metacyclic automorphism groups" Northeast. Math. J.14. 5-8 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Naoki Chigira: "Finite groups whose abelian subgroups have consecutive orders" Osaka J. Math.35. 439-445 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Naoki Chigira: "Non abelian sylow subgroups of finite groups of even order" ERA Amer. Math. Soc.4. 88-90 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Naoki Chigira: "Sharp characters and Brauer characters" J.Group Theory. 1. 363-368 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Giga: "On strong maximum principle and large time behavior of generalized mean curvature flow with Neumanr boundary condition" Journal of Differential Equations. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Takegahara: "On Butler's unimodality result" Combinatorica. 18. 437-439 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "Maass Dirichelt series for Siegel modular forms(after Arakawa)" Proc.of 1st Number Theory Autumn Workshop. (in press). (1999)

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

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "An explicit formula for Siegel series" Amer.J.Math.121(in press). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "A power series attached to local densities of forms of higher degree" Hong Kong Math.J.2(in press). (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Ibukiyama: "Koecher-Maass Dirichlet series for Eisenstein series of Klingen type" Recearch Report of R.I.M.S.965. 41-51 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "Squared Mobius function for half-integral matrices" Contemporary Math.(to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.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
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "A remark on Kitaoka formal power series attached to local densities" Manuscripta Math.92. 477-486 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "A recursion formula for local densities of quadratic forms" J.Number Theory. 60. 183-210 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "A recursion formula for local densities with congruence conditions" Memoirs of the Muroran Inst.of Tech.47. 97-102 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "An explicit formula for the Fourier coefficients of Siegel Eisentein series" Research Report of R.I.M.S.1002. 55-69 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "A square Moebius function over quadratic forms and its applications to Siegel modular forms" Proc.of 5-th International Conference on Finite or Infinite Dimensional Complex Analysis. 151-155 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Katsurada: "A Short proof of Kitaoka-Feit Induction lemma for Siegel series" Abhandlungen aus dem Mathematishen Slmiror der Universitat Hamburg. 68. 297-304 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Katsurada: "A Power series associated with local densities of forms of higher degue" Bulletin of the Hong Kong Mathematical Society. 2. (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Katsurada: "An explicit formula for Siegel series" American Journal of Mathematics. 121. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 伊吹山知義: "Koecher-Maass Dirichtet series for Eisensfein series of Klingen type" 数理解析研究所講究録. 965. 41-51 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 桂田英典: "An integral expression of koecher-Maass Dirichletseries and its applications(after T.Arakawa)" 第1回整数論オータムワークショップ報告集. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Takegahara: "On Butler's unimodality result" Combinatorica. 18. 437-439 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 竹ケ原 裕元: "On the number of crossed homomorphisms from a finite cyclic p-group to a finite p-group" 数理解析研究所講究録. 1057. 38-40 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] G.Chen: "Finite groups with metacyclic automorphism groups" Northeast.Math.J.14. 5-8 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Naoki Chigira: "Finite groups whose abelian Subgroups have consecutive orders" Osaka J.Math.35. 439-445 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Naoki Chigira: "Non abelian Sylow Subgroups of finite groups of even order" ERA Amer.Math.Soc.4. 88-90 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Naoki Chigira: "Sharp characters and Brauer characters" J.Group Theory. 1. 363-368 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Giga: "On strong maximum principle and large time behavior of generalized mean curvature flow with Neumanr boundary condition" Journal of Differential Equations. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Takegahara: "On Butler's unimodality result" Combinatorica. 18. 437-439 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hidenori Katsurada: "A recursion fornula for local densities" Jourmal of Number Theory. 64. 183-210 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hidenori Katsurada: "A remark on Kitaoka formal power sevies attached to local densities" Manuscripta Mathematica. 92. 477-486 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hidenori Katsurada: "An explicit formula for the Fourier coefficients of Siegel Eisenstein series of degree 3" Nagoya Mathematical Journal. 146. 199-223 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hidenori Katsurada: "A recursion formula of local densities with congruence conditions" 室蘭工業大学紀要. 47. 97-102 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hidenori Katsurada: "An explicit formula for the Fourier coefficients of Siegel Eisenstein series" 数理解析研究講究録. 1002. 55 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 俵我美一, 大沼正樹, 佐藤元彦: "柱状領域での等高面平均曲率流方程式のノイマン問題の解の時間無限大での" 日本数学会1997年度年会函数方程式論分科会講演アブストラクト. 86-87 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Naoki Chigira: "Generating alfernating groups" Hokkaido Mathematical Journal. 26. 435-438 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Naoki Chigira: "Number of Sylow subgroups and p-nilpotence of finite groups" Journal of Algebra.

    • Related Report
      1997 Annual Research Report
  • [Publications] Naoki Chigira: "Finite groups whose abeliau subgroups have consecutive orders" Osaka Journal of Mathematics.

    • Related Report
      1997 Annual Research Report
  • [Publications] Guiyun Chen, Naoki Chigira and Hiroyoshi Yamaki: "Finite groups with metacyclic automorphism groups" Northeastern Mathematical Journal.

    • Related Report
      1997 Annual Research Report
  • [Publications] Naoki Chigira and Nobuo Iiyori: "Prime graphs and Brauer characters." Journal of Group Theory.

    • Related Report
      1997 Annual Research Report
  • [Publications] 竹ヶ原 裕元: "The number of hemoworphisms,from a finite abelian group to a finite group" 数理解析研究所講究録. 991. 171-179 (1997)

    • Related Report
      1997 Annual Research Report

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

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