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Research on automorphic forms

Research Project

Project/Area Number 62540039
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionKyoto University

Principal Investigator

YOSHIDA Hiroyuki  Department of mathematics, Faculty of Science, Kyoto Univ. Associate Professor, 理学部, 助教授 (40108973)

Co-Investigator(Kenkyū-buntansha) MARUYAMA Masaki  Associate Professor, Dept. of Math. Fac. of Sci Kyoto Univ., 理学部, 助教授 (50025459)
UENO Kenji  Professor, Dept. of Math. Fac. of Sci Kyoto Univ., 理学部, 教授 (40011655)
UEDA Masaru  Instructor, Dept. of Math. Fac. of Sci Kyoto Univ., 理学部, 助手 (80193811)
ISHII Hidenori  Instructor, Dept., of Math. Fac. of Sci., Kyoto Univ., 理学部, 助手 (60159671)
HIJIKATA Hiroaki  Professor, Dept. of Math., Fac. of Sci. Kyoto Univ, 理学部, 教授 (00025298)
永田 雅宜  京都大学, 理学部, 教授 (00025230)
Project Period (FY) 1987 – 1988
Project Status Completed (Fiscal Year 1988)
Budget Amount *help
¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1988: ¥900,000 (Direct Cost: ¥900,000)
KeywordsAutomorphic form / L-function / Unitarizability / ユニタリー表現 / 明示公式 / 2次形式
Research Abstract

H. Yoshida has investigated representations of finite groups on Siegel modular forms in terms of theta series and generalized Hecke's theory. He has calculated zeros of various L-functions associated with automorphic forms. He also determined unitarizable principal series representations completely for p-adic Chevalley groups of classical type.
H. Hijikata has proved that the restriction to an anisotropic torus of an arbitrary smooth irreducible representation of GL(2) over a p-adic field is multiplicity free. He (with A.Pizer, T. Schemanske) has obtained a definitive result on the classical basis problem on theta series.
M.Ueda has obtained interesting results on modular forms of half integral weight, using twisting poerators. His results suggest the existence of the theory of new forms also for the half integral weight case.
H. Ishii proved a criterion for the non-existence of an abelian variety with everywhere good reduction.

Report

(2 results)
  • 1988 Annual Research Report   Final Research Report Summary
  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] H.Yoshida.: J.of Math.Kyoto University. 28. 343-372 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] H.Yoshida.: Proc.of Japan Academy,Ser.A. 63. 396-399 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] H.Yoshida.: J.Ramanajun Math.Soc.(Ramanujan Birth Centennary Special Issue). 3. 87-95 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] H.Hijikata,;A.Pizer,;T.Shemanske.: Memoire Amer.Math.Soc.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] M.Ueda.: J.of Math.Kyoto Univ.28. 505-555 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] H.Ishii.: Japanese J.of Math.15.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hiroyuki Yoshida: "On representations of finite groups in the space of Siegel modular forms and theta series" J. of Math. Kyoto University. 28. 343-372 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hiroyuki Yoshida: "On a certain distribution on GL(n) and explicit formulas" Proc. of Japan Academy, Ser. A. 63. 396-399 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hiroyuki Yoshida: "On calculations of zeros of L-functions related with Ramanujan's discriminant function on the critical line" J. Ramanujan Math. Soc.3. 87-95 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hiroaki Hijikata, A. Pizer, T. Shemanske: "The basis problem for modular forms on _o(N)" Memoire Amer. Math. Soc.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Masaru Ueda: "The decomposition of the space of cusp forms of half integral weight and trace formula of Hecke operators" J. of Math. Kyoto University. 28. 505-555 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hiroyuki,Yoshida: Proceedings of the Japan Acad.,Ser.A.63. 396-399 (1987)

    • Related Report
      1988 Annual Research Report
  • [Publications] Hiroyuki,Yoshida: Kyoto Journal of Math.28. (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] Hiroaki,Hijikata: Volume dedicated to Prof.M.Nagata.

    • Related Report
      1988 Annual Research Report

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Published: 1988-04-01   Modified: 2016-04-21  

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