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Investigation of Koecher-Maass series for various liftings of Siegel modular forms

Research Project

Project/Area Number 13640003
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

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

Co-Investigator(Kenkyū-buntansha) HASEGAWA Yuji  Muroran Institute of Technology, Associate Professor, 工学部, 助教授 (30287982)
YAMAZAKI Noriaki  Muroran Institute of Technology, Lecturer, 工学部, 講師 (90333658)
TAKEGAHARA Yugen  Muroran Institute of Technology, Professor, 工学部, 教授 (10211351)
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥4,100,000 (Direct Cost: ¥4,100,000)
Fiscal Year 2002: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2001: ¥2,100,000 (Direct Cost: ¥2,100,000)
KeywordsMaass zeta function / Ikeda lifting / Eisenstein series / Squared Moebius function / Standard zeta function / Ikeda-Miyawaki life / Ikeda-Miyawaki lift
Research Abstract

1. In 2000, we gave an explicit formula for the Koecher-Maass Dirichlet series for the Ikeda lifting of an elliptic cuspidal Hecke-eigenforms f jointly with T. Ibukiyama. We gave some result on the algebraicity of special values of a certain Dirichlet series attached to f appearing in such a formula. 2. We gave a good sufficient condition for two Siegel cuspidal Hecke-eigenforms to coincide with each other. This result is slightly stronger than the result which we gave in 1999. Furthermore, we proposed a certain conjecture on a refinement of the above result, and proved this conjecture under a certain condition on the non-vanishing of the Koecher-Maass series.
3. By using the pullback formula for Siegel Eisenstein series, the differential operators due to Ibukiyama, and an explicit formula for Siegel series due to Katsurada, we gave an exact values of the standard zeta function of a modular form f twisted by a character χ in the following cases:
(1) f is an elliptic cuspidal Hecke eigenform of neben type, and χ is a Dirichlet character of prime conductor.
(2) f is a Siegel modular form of degree 2 of level 1, and χ is the trivial character.
4. We proved that the p-adic Eisenstein series of degree 2 defined by Nagaoka is a true modular form (Joint work with S. Nagaoka.)
5. We investigated the action of Hecke operator on the theta series (Joint work with R. Schulze-Pillot.)

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (62 results)

All Other

All Publications (62 results)

  • [Publications] T.Ibukiyama: "Squared Moebius function for half-integal matrices and its applications"Journal of Number Theory. 86. 78-117 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H.Katsurada: "Euler factor of a certain Dirichiet series attached to Siegel Eisenstein series"Abhandlungen aus dem Mathematischen Seminar der Universitaet Hambrug. 71. 81-90 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H.Katsurada: "Siegel保型形式の様々な持ち上げに付随するKoecher-Maass級数"RIMS Kokyuroku. 1238. 63-68 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H.Ishihara: "p-divisibility of the number of solutions of x^p=1 in a symmetric group"Ann.Comb.. 5. 197-210 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Asai: "|Hom(A, G)|, IV"J.Algebra. 246. 543-563 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Takegahara: "A generating function for the number of homomorphisms from a finitely generated abelian group to an alternating group"J.Algebra. 248. 554-574 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Takegahara: "On P. Hall's relations in finite groups"RIMS Kokyuroku. 1214. 27-36 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] A.Ito: "Time-dependent attractors of bounded dynamical systems generated by subdifferentials"Communications in Applied Analysis. 5. 403-419 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] N.Yamazaki: "Almost periodic stability for doubly nonlinear evolution equations generated by subdifferentials"Nonlinear Anal.TMA.. 47. 1725-1763 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 山崎教昭: "ダム問題に対する時間概周期解"RIMS Kokyuroku. 1197. 163-175 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 山崎教昭: "Attractors for non-autonomous systews without uniquness"第23回発展方程式若手セミナー報告集. 18-23 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H.Katsurada: "Exact values of the standard zeta functions"Proc.of Japanese-German Seminar "Explicit Structures of Modular Forms and Zeta Functions". 32-41 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H.Katsurada: "Special values of the standard zeta functions"Galois Theory and Modular Forms. (to appear). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H.Katsurada: "A remark on the coincidence of Hecke eigenforms"Comm.Math.Univ.St.Pauli. 52. 47-54 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Asai: "On the number of cocycles for dihedral groups"RIMS Kokyuroku. 1251. 70-82 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 竹ヶ原 裕元: "置換表現の数え上げと母関数"第47回代数学シンポジウム報告集. 5-16 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Okazaki: "Numerical results for the dam problem in two dimensional case"GAKUTO Intern.Ser.Math.Appl.. 17. 291-305 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] N.Kenmochi: "Global attractors for multivalued flows associated with subdifferentials"Proc.of the 4th European Conference. 248. 135-144 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] N.Yamazaki: "Attractors for non-autonomous multivalued evolution systems generated by time-dependent subdifferentials"Abstract and Applied Analysis. 7. 453-473 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Baker: "Automorphisms of X^*_0(p)"Journal of Number Theory. 72-87 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Ibukiyama: "An explicit formula for Koecher-Maass Dirichlet seris for Eisenstein series of Klingen type"Journal of Number Theory. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Asai: "Crossed homomorphisms from rank 2 abelian to exceptional p-groups"Journal of Algebra. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H. Katsurada: "Euler factor of a certain Dirichlet series attached to Siegel Eisenstein series"Abh. Math. Sem. Univ. Hamburg. 71. 81-90 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H. Katsurada: "Exact values of the standard zeta functions"Proc. Of Japanese-German Seminar "Explicit Structures of Modular Forms and Zeta Functions". 32-41 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H. Katsurada: "A remark on the coincidence of Hecke eigenforms"Comment. Math. Univ. St. Pauli. 52. 47-54 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H. Katsurada: "Dirichlet series for various liftings of Siegel modular forms"RIMS Kokyuroku. 1238. 63-68 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Asai, Y. Takegahara: "-Hom(A,G)-, IV"J. Algebra. 246. 543-563 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H. Ishihara, H. Ochiai, Y. Takegahara, T. Yoshida: "p-divisibility of the number of solutions of x^p = 1 in a symmetric group"Ann. Comb.. 5. 197-210 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y. Takegahara: "On P. Hall's relations in finite groups"RIMS Kokyuroku. 1214. 27-36 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y. Takegahara: "A generating function for the number of homomorphisms from a finitely generated abelian group to an alternating group"J. Algebra. 248. 554-574 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Asai, Y. Takegahara, T. Niwasaki: "On the number of cocycles for dihedral groups"RIMS Kokyuroku. 1251. 70-82 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] A. Ito, N. Kenmochi, N. Yamazaki: "Time-dependent attractors of bounded dynamical systems generated by subdifferentials"Communications in Applied Analysis. 5. 403-419 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] N. Yamazaki: "Almost periodic stability for doubly nonlinear evolution equations generated by subdifferentials"Nonlinear Anal. TMA.. 47. 1725-1736 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] N. Yamazaki: "Attractors for non-autonomous multivalued evolution systems generated by time-dependent subdifferentials"Abstract and Applied Analysis. 7. 453-473 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] N. Yamazaki, Takahashi, T. Okazaki: "Time-dependent almost periodic solutions to dam problems"RIMS Kokyuroku. 1197. 163-175 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] N. Yamazaki: "Attractors for non-autonomous systems without uniqueness"Proc. Of 23-th Young Mathematicians Seminar on Evolution Equations. 18-23 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M. Baker, Y. Hasegawa: "Automorphisms of X^*_0(p)"J. Number Theory. 100. 72-87 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Ibukiyama, H. Katsurada: "An explicit formula for Koecher-Maass Dirichlet series for Eisenstein series of Klingen type"J. of Number Theory. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Asai, T. Niwasaki, Y. Takegahara: "Crossed homomorphisms from rank 2 abelian to exceptional p-groups"J. of Algebra. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H. Katsurada: "Special values of the standard zeta functions. In Galois Theory and Modular Forms"Kluwer Academic Publishers. 337-356 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Okazaki, N. Yamazaki: "Numerical results for the dam problem in two dimentional case. In The 2nd Polish-Japanese Days on Mathematical Aspects of Modelling Structure Formation Phenomena, GAKUTO Intern. Ser. Math. Appl., vol 17"Gakkotosho. 291-305 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] N. Kenmochi, N. Yamazaki, ed. J. Bemelmans, et al: "Global attractors for multivalued flows associated with subdifferentials. In Elliptic and Parabolic Problems, Proceeding of the 4th European Conference, Rolduc, Netherlands, Gaeta, Italy, 2001"World Scientific. 135-144 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H.Katsurada: "Special values of the standard zeta functions"Galois Theory and Modular Forms. (to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Katsurada: "A remark on the coincidence of Hecke eigenforms"Comm. Math. Univ. St. Pauli. (to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Asai: "On the number of cocycles for dihedral groups"RIMS Kokyuroku. 1251. 70-82 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 竹ケ原 裕元: "置換表現の数え上げと母関数"第47回代数学シンポジウム報告集. 5-16 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Okazaki: "Numerical results for the dam problem in two dimensional case"GAKUTO Intern. Ser. Math. Appl.. 17. 291-305 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] N.Kenmochi: "Global attractors for multivalued flows associated with subdifferentials"Proc. of the 4th European Conference. 248. 135-144 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] N.Yamazaki: "Attractors for non-autonomous multivalued evolution systems generated by time-dependent subdifferentials"Abstract and Applied Analysis. 7. 453-473 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Baker: "Automorphisms of X_0^*(p)"Journal of Number Theory. (to Appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Ibukiyama, H. Katsurada: "Squared Moebius function for half-integal matrices and its applications"Journal of Number Theory. 86. 78-117 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Katsurada: "Euler factor of a certain Dirichlet series attached to Siegel Eisenstein series"Abhandlungen aus dem Mathematischen Seminar der Universitaet Hambrug. 71. 81-90 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Katsurada: "Siegel保型形式の様々な持ち上げに付随するKoecher-Maass級数"数理解析研究所講究録. 1238. 63-68 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Ishihara, H.Ochiai, Y.Takegahara, T.Yoshida: "p-divisibility of the number of solutions of x^p=1 in a symmetric group"Ann.Comb.. 5. 197-210 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Asai and Y. Takegahara: "|Hom(A,G)|,IV"J. Algebra. 246. 543-563 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Takegahara: "A generating function for the number of homomorphisms from a finitely generated abelian group to an alternating group"J. Algebra. 248. 554-574 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Takegahara: "On P. Hall's relations in finite groups"数理解析研究所講究録. 1214. 27-36 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] A.Ito, N.Kenmochi and N.Yamazaki: "Time-dependent attractors of bounded dynamical systems generated by subdifferentials"Communications in Applied Analysis. 5. 403-419 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] N.Yamazaki: "Almost periodic stability for doubly nonlinear evolution equations generated by subdifferentials"Nonlinear Anal. TMA.. 47. 1725-1763 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 山崎教昭, 高橋正人, 岡崎貴宣: "ダム問題に対する時間概周期解"数理解析研究所講究録. 1197. 163-175 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 山崎教昭: "Attractors for non-autonomous systems without uniquness"第23回発展方程式若手セミナー報告集. 18-23 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 山崎教昭: "障害物問題に対応する多価力学系について"第27回発展方程式研究会報告集. 印刷中. (2002)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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