• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

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
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 2000: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1999: ¥2,000,000 (Direct Cost: ¥2,000,000)
KeywordsMaass zeta function / Ikeda lifting / Eisenstein series / Squared Moebius function / Standard zeta function / オイラー積 / スタンダードゼータ関数 / トリプルL関数 / 特殊値 / ケツヒヤー.マースゼータ関数 / 斎藤・黒川リフテイング / クリンゲン・アイゼンシユタイン級数
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.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (56 results)

All Other

All Publications (56 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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 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. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [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
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Katsurada: "On the coincidence of Heche-eigen forms"Abhand lungen cuis dem Mathematischen Seminar der Umiversitat Hamburg. 70. 77-83 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Ibukiyamici: "Squared Mobius function for half-integral matrios and its applications"Journal of Number Theory. 86. 78-117 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Katsurada: "Euler factor of a certain Divichelet sevies attached to Siegel Eisenstem sevies"Abhand lungen cuis dem Mathemtischen Seminar der Umiversitat Hamburg. 71. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Katsurada: "Dirichlet series for Siegel modular forms and quadratic forms""Codes, Lattices, Modular forms and vertex operator algebras"シンポジウム報告集. 107-115 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] Hidencri KATSURADA: "The number of homomorphisms from a tinite abelian group to a symmetric group"Communications in Algebrc.. 28. 2291-2290 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Yugen TAKEGAHARA: "The number of subgroups of a finite group"Journal of Algebra. 227. 783-796 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Naoki CHIGIRA: "The number of homomorphisms from a finite group to a general linear group"Journal of Algebra. 232. 236-254 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Yugen TAKEGAHARA: "On Wohlfahrt formula for finite abelian groups"Formal Power Series and Algebraic Combinatrics Proceeding, Seringer. 754-764 (2000)

    • Related Report
      2000 Annual Research Report
  • [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)

    • Related Report
      2000 Annual Research Report
  • [Publications] Yosikaza Giga and Motohiko Sato: "A level set approach to semicontinuous viscosity solutions for cauchy problems"Communications in partial differential equations.

    • Related Report
      2000 Annual Research Report
  • [Publications] Tomoyoshi Ibukiyama: "An explicit form of Koecher Maal's Dirichlet series for Klingen's Eisenstein Series"Manuskripite der Forshergruppe Arithmetik.. 12. 1-38 (1999)

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

    • Related Report
      1999 Annual Research Report
  • [Publications] Hidenori Katsurada: "On the coincidence of Hache eigenfans"Abhandlungen aus dem Mathematischen Seminor der Univesitat Hamburg. 70. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Tsunenobu Asai: "On the number of crossed homomorphisms"Hokkaido Mathematical Journal. 28. 535-543 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Yugen Takegahara: "On the Frobenius numbers of Symmetric groups"Journal of Algebra. 221. 551-561 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Naoki Chigira,Nobuo Iiyori,Hiroyoshi Yamaki: "Non-abelian Sylow subgroups of finite groups of even order"Invent. Math.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Giga,M.H.Sato: "On semicontinuous solutions for general Hamilton-Jacobi equations"Proceedings of Japan Academy. 75. 159-162 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 儀我美一,佐藤元彦: "Semicontinuous solution for Hamilton-Jacobi equations with general Hamiltonians"数理解析研究所講究録「特異点論と微分方程式」. 1111. 117-124 (1999)

    • Related Report
      1999 Annual Research Report

URL: 

Published: 1999-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi