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Automorphic forms of several variables and spherical functions of homoge-neous spaces

Research Project

Project/Area Number 09440016
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKOBE UNIVERSITY

Principal Investigator

YAMAZAKI Tadashi  Kobe University Faculty of Science Professor, 理学部, 教授 (30011696)

Co-Investigator(Kenkyū-buntansha) MURASE Atsushi  Kyoto Sangyo University Faculty of Science Professor, 理学部, 教授 (40157772)
SUGANO Takashi  Kanazawa University Faculty of Science Professor, 理学部, 教授 (30183841)
SEKIGUCHI Hideko  Kobe University Faculty of Science, 理学部, 助手 (50281134)
TAKAYAMA Nobuki  Kobe University Faculty of Science Professor, 理学部, 教授 (30188099)
SAITO Masahiko  Kobe University Faculty of Science Professor, 理学部, 教授 (80183044)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥8,600,000 (Direct Cost: ¥8,600,000)
Fiscal Year 1998: ¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 1997: ¥5,100,000 (Direct Cost: ¥5,100,000)
Keywordsautomorphic form / Hecke algebra / spherical function
Research Abstract

The spherical function or the Shintani function of homogeneous spaces are important in order to study the Fourier expansion of period of automorphic forms and L-functions associated to automorphic forms.
We studied mainly the Shintani function of the classical groups. in particular we proved uniqueness and existence of the Shintani function and in some cases we obtained explicit formulas for them. We applied them to examine analytic and arithmetic properties of automorphic L-functions. (Muarase-Sugano)
It would be our next objective to define suitable geometrical objects associated to spherical subgroups and to interpret the Shintani function in terms of their cohomology groups.

Report

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

    (26 results)

All Other

All Publications (26 results)

  • [Publications] A.Murase: "On standard L-functions attached to automorphic forms on definite orthogonal groups" Nagoya Mathematical Journal. (印刷中). (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Saito: "Signature defects and eta functions of degenerations of abelian varieties" Japan.J.Math.23-2. 319-364 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Watanabe: "Cousin problems and holomorphic cocycles" Math.Japonica. 48-2. 217-221 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Sekiguchi: "Compactifications of the configuration space of b points of the projective plane" Tohoku Mathematical Journal. 49. 379-413 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] B.Sturmfels: "Grobner bases and hypergeometric functions" London Mathematical Society Lecture Notes Series. 251. 246-258 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Saito: "Hypergeometric polynomials and Integer Programming" Compositio Math.(印刷中). (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Saito: "Grobner deformations of hypergeometric differential equations" Springer verlag(印刷中), (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Murase: "On standard L-functions attached to auto-morphic forms on definite orthogonal groups" Nagoya Mathematical Journal. (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] M.Saito: "Signature defects and eta functicons of degen-erations of abelian varieties" Japan.J.Math.23. 319-364 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Watanabe: "Cousin problems and holomorphic cocy-cles" Math.Japonica. 48. 217-221 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Sekiguchi: "Compactifications of the configuration space of 6 points of the projective plane" Tohoku Mathematical Journal. 49. 379-413 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] B.Sturmfels: "Grobner bases and hypergeometric func-tions" London Mathematical Society Lecture Notes Series. 251. 246-258 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Toshinori Oaku: "An algorithm for de Rham cohomol-ogy groups of the complement of an affine variety via D-module computation" Journal of Pure and Applied Algebra. (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] M.Saito: "Hypergeometric polynomials and Integer Pro-gramming" Compositio Math.(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] M.Saito: "Grobner deformations of hypergeometric dif-ferential equations" Springer verlag. (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] A.Murase: "On standard L-functions attached to automorphic forms on definite orthogonal orthogonal groups" Nagoya Mathematical Journal. (印刷中). (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Saito: "Signature defects and eta functicons of degenerations of abelian varieties" Japan.J.Math.23-2. 319-364 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Watanabe: "Cousin problems and holomorphic cocycles" Math.Japonica. 48-2. 217-221 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] J.Sekiguchi: "Compactifications of the configuration space of 6 points of the projective plane" Tohoku Mathematical Journal. 49. 379-413 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] B.Sturmfels: "Grobner bases and hypergeometric functions" London Mathematical Society Lecture Notes Series. 251. 246-258 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Saito: "Hypergeometric polynomials and Integer Programming" Compositio Math.(印刷中). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Saito: "Grobner deformations of hypergeometric differential equations" Springer verlag (印刷中), (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.-H Saito: "Signature defects and eta functions of degenerations of abelian varieties" Japanese Journal of Mathematics. 23. 319-364 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Takayama: "Hypergeometric polynomials and Integer Programming" Compositio Mathematica. (to appear). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] A.Murase: "On standard L-functions attached to automorphic forms on definite orthogonal groups" Nagoya Mathematical Journal. (to appear). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Takayama: "Compactifications of the configuration space of 6 points of the projective plane and fundamental solutions of the hypergeometric system of type (3, 6)" Tohoku Mathematical Journal. 49. 379-413 (1997)

    • Related Report
      1997 Annual Research Report

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

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