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2000 Fiscal Year Final Research Report Summary

Investigation of Dirichlet series for Siegel modular forms

Research Project

Project/Area Number 11640002
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) 1999 – 2000
KeywordsMaass zeta function / Ikeda lifting / Eisenstein series / Squared Moebius function / Standard zeta function
Research Abstract

(1)Using the squared Moebius function for half-integral matrices defined by H.Katsurda result of 1, we gave an explicit formula for the Koecher-Maass Dirichlet series attached to the Klingen-Eisenstein lifting of even degree of an elliptic cuspidal Hecke-eigenform f.(Joint work with T.Ibukiyama.)In this explicit formula, there appears a certain Dirichlet series of two variables attached to f, which was originally investigated by W.Kohnen and D.Zagier. Furthermore, by using the same method, we gave also an explicit formula in the case of the Klingen-Eisenstein lifting of odd degree. In this formula, there appears a new type of Dirichlet series of two variables attached to f.
(2)T.Ikeda gave a generarization of the Saito-Kurokawa lifting of an elliptic cuspidal Hecke-eigenform f, and constructed a certain Siegel cusp form, called the Ikeda lifint of f. We gave an explicit formula for the Koecher-Maass series for the Ikeda lif of f.(Partly joint work with T.Ibukiyama.)
(3)We gave a good sufficient condition for two Siegel cuspidal Hecke-eigenforms to conincide with each other. 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.
(4)We proved that a zeta function of Andrianov type for the Siegel-Eisenstein series has Euler product, and determined a 'good' Euler factor of it.

  • Research Products

    (38 results)

All Other

All Publications (38 results)

  • [Publications] H.Katsurada: "An explicit formula for Siegel series"American Journal of Mathematics. 121. 415-452 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Katsurada: "A power series attached to local densities of forms of higher degree"Hong Kong Mathematical Journal. 2. 297-304 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Katsurada: "Squared Mobius function for half-integral matrices"Comtemporary Mathematics. 249. 235-248 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Katsurada: "On the coincidence of Hecke-eiglu forms"Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg. 70. 77-83 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Ibukiyama: "Squared Mobius function for half-integral 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
  • [Publications] H.Katsurada: "Euler factor of a certain Dinchref series attached to siegel Esenstein Series"Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg. 71. (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yugen TAKEGAHARA: "On the Frobenius numbers of symmetric group"Journal of Algebra. 221. 551-561 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tsunenobu ASAI: "On the number of crossed homomorphisms"Hokkaido Mathematical Journal. 28. 535-543 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hidenori KATSURADA: "The number of homomorphisms from a finite abelian group to a symmetric group."Communications in Algebra. 28. 2271-2290 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yugen TAKEGAHARA: "The number of subgroups of a finite group"Journal of Algebra. 227. 783-796 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Naoki CHIGIRA: "The number of homomorphisms from a finite group to a general linear group"Journal of Algebra. 232. 236-254 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yugen TAKEGAHARA: "On Wohltahrt formula for finite abeliam groups"Formal Power Series and Algebraic Combinatorics Proceedings, Soringer. 754-764 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Giga and Motohito Sato: "A level set approach to semicontinuous viscosity solutions for canchy problems"Communications in partial differential equations.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Naoki Chigira: "Non-abelian Sylow subgroups of finite groups of even order"Invent.Math.. 139. 525-539 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 千吉良直紀: "PRIME GRAPHS AND ODD ORDER SUBGROUPS OF SIMPLE GROUPS"第45回代数学シンポジウム報告集. 185-193 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Katsurada: "On the coincidence of Hecke-eigen forms"Abh.Math.Sem.Hamburg. 70. 77-83 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Ibukiyama and H.Katsurada: "Squared Mobius function for half-integral matrices and its applications"J.Number Theory. 78-117 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Katsurada: "Euler factor of a certain Dirichlet series attched to Siegel Eisenstein series"Abh.Math.Hamburg. 71(to appear). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Katsurada: "Squared Mobius function for half-integral matrices"Contemporary Math.. 249. 235-248 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Katsurada: "A power series attached to local densities of forms of higher degree"Hong Kong Math.J.. 2. 297-304 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Katsurada: "An explicit formula for Siegel series"Amer.J.Math.. 121. 415-452 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Katsurada: "Dirichlet series for Siegel modular forms and quadratic forms"Proc.of Conference "Codes, Lattices, Modular Forms and Vertex Operator Algebras". 107-115 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Katsurada: "Fourier coefficients of Eisenstein series"Proc.2nd Autumn Workshop on Number Theory. 35-66 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Ibukiyama and H.Katsurada: "An explicit form of the Koecher-Maaβ Dirichler series for Klingen's Eisenstein series, Manuskripte der Forschergruppe Arithmetik"Heidelberg-Mannheim. 12. 1-38 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Ibukiyama and H.Katsurada: "Squared Mobius function for half-integral matrices and its applications, Manuskripte der Forschergruppe Arithmetik"Heidelberg-Mannheim. 8. 1-38 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Katsurada: "Maass Dirichlet series for Siegel modular forms(after Arakawa)"Proc.of 1st Autumn Workshop on Number Theory. 116-129 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Asai and Y.Takegahara: "On the number of crossed homomorphisms"Hokkaido Math.J.. 28. 535-543 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Takegahara: "On the Frobenius numbers of symmetric groups"J.Algebra. 221. 551-561 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Katsurada, Y.Takegahara and T.Yoshida: "The number of homomorphisms from a finite abelian group to a symmetric group"Comm.Algebra. 28. 2271-2290 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Takegahara: "The number of subgroups of a finite group"J.Algebra. 227. 783-796 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N.Chigira, Y.Takegahara and T.Yoshida: "The number of homomorphisms from a finite group to a general linear group"J.Algebra. 232. 236-254 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yugen Takegahara: "On Wohlfahrt formula for finite abelian groups, Formal Power Series and Algebraic Combinatorics"12 th International Conference, FPSAC'00, Moscow, Russia, Proceedings, Springer. 754-764 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Takegahara: "A generating function for the number of homomorphisms from a finitely generated abelian group to an alternating group"J.Algebra. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yugen Takegahara: "The number of subgroups of a finite p-group"Proceedings of R.I.M.S Symposium. 1140. 136-139 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yugen Takegahara: "p-adic properties of the Frobenius numbers of symmetric groups"Proceedings of the 17th Algebraic Combinatorics Symposium. 62-71 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Naoki Chigira, Nobuo Iiyori and Hiyoyoshi Yamaki: "Non-abelian Sylow subgroups of finite groups of even order"Invent.Math. 139. 525-539 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Naoki Chigira: "Prime graphs and odd order subgroups of simple groups(in Japanese)"Proceedings of the 45th Algebra Symposium. 185-193 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Giga and M.Sato: "A level set approach to semicontinuous viscosity solutions for Cauchy problems"Communications in Partial Differential equations. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2002-03-26  

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