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Research on automorphic representations

Research Project

Project/Area Number 06402001
Research Category

Grant-in-Aid for Scientific Research (A)

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

Principal Investigator

YOSHIDA Hiroyuki  Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40108973)

Co-Investigator(Kenkyū-buntansha) UMEDA Toru  Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (00176728)
HIRAI Takeshi  Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70025310)
HIRAGA Kaoru  Kyoto Univ., Graduate School of Science, Instructor, 大学院・理学研究科, 助手 (10260605)
IKEDA Tamotsu  Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (20211716)
HIJIKATA Hiroaki  Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00025298)
Project Period (FY) 1994 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥11,800,000 (Direct Cost: ¥11,800,000)
Fiscal Year 1996: ¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 1995: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 1994: ¥4,800,000 (Direct Cost: ¥4,800,000)
KeywordsL-function / Lie group / period of an abelian variety / semisimple Lie群 / 保型形式 / 周期 / 保型表現 / モジュラー形式
Research Abstract

H.Yoshida studied periods of Hilbert modular forms and proved Shimura's conjectures on P,Q-invariants. He also studied the derivatives of Artin's L-functions at s=0 and found a relation with periods of abelian varieties with complex multiplication. This relation can be sharpened by the notion of "absolute CM-periods".
T.Ikeda studied residues of Eisenstein series and proved a Siegel-Weil type formula when Eisenstein series does not converge.
K.Hiraga studied the multiplicity of a discrete series representation with which it occurs in L^2 (GAMMA/G), where G is a semisimple Lie group and GAMMA is a discrete subgroup.
T.Umeda studied the notion of dual reductive pair in the case of quatum groups ; he generalized Capelli type identities for this case.
H.Hijikata conjectured an approximation theorem for semisimple algebras over the quotient field of a Dedekind domain ; related with this conjecture, he obtained many results on orders and lattices.

Report

(4 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • 1994 Annual Research Report
  • Research Products

    (30 results)

All Other

All Publications (30 results)

  • [Publications] H. Yoshida: "On a conjecture of Shimura concrning periods of Hilbcrt modular farms" Amer, J. Math.117. 1019-1038 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H. Yoshida: "On calculations of zeros of various L-functions" J. Math. Kyoto University. 35. 663-696 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H. Hijikata: "On the decomposition of latlius over orders" J. Math. Soc, Japan. 49. (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T. Ikeda: "On the residue of Eiscnstein series and the Siegl-Weil formula" Comp. Math.103. 183-218 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K. Hiraga: "On the multiplicities of the discrete series of semisimple Lie groups" Dukc Math. J.85. 167-181 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T. Umeda (with Noumi, Wakayama): "Dual pairs, spberical barmonicas, and a Capolliidentity in quantum group" Comp. Math.104. 227-277 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H.Yoshida: "On a conjecture of Shimura concerning periods of Hilbert modular forms" Amer.J.Math.117. 1019-1038 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H.Yoshida: "On calculations of zeros of various L-functions" J.Math.Kyoto Univ.35. 663-696 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H.Hijikata: "On the decomposition of lattices over orders" J.Math.Soc.Japan. Vol.49. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Ikeda: "On the residue of the Eisenstein series and the Siegel-Weil formula" Comp.Math.103. 183-218 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Hiraga: "On the multiplicities of the discrete series of semisimple Lie groups" Duke Math.J.85. 167-181 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Noumi, T.Umeda and M.Wakayama: "Dual pairs, spherical harmonics, and a Capelli Identity in quantum group theory" Comp.Math.104. 227-277 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H.Yoshida: "On absolute CM-pcriods" 数理解析研究所講究録. 965. 87-133 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Ikeda: "On the residue of the Eisenstein series and the Siegel-Weil formula" Compositio Mathematica. 103. 183-218 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] K.Hiraga: "On the multiplicities of the discrete series of semisim plelie groups" Du/Te Mathematical Journal. 85. 167-181 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Hirai: "Relation between unitary repre sentations of diffeo morphism groups and those of the infinite symmetric group" Proc.of Japan-Germany Symp on harmonic analpis. 94-112 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Umeda(with Noumi and Wakayama): "Dual pairs,spherical harmonics,and a Capelli I dentity in quantum group theory" Comp.Math. 104. 227-277 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Hijikata: "On-the decemposilion of lattices over orders" Journal of Math.Soc.Japan. 49-3(発表予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] H. Yoshida: "On a conjecture of Shimura concerining periods of Hilbert modular forms" American Journal of Mathematics. 117. 1019-1038 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] H. Yoshida: "On calculations of zeros of various L-funcrtions" Journal of Mathematics of Kyoto University. 35. 663-696 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] T. Ikeda: "On the residue of the Eisenstein senes and the Siegal-Weil formula" Compositio Mathematica. (発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] K. Hiyaga: "On the multiplicities of the discrete series of semisimple Lie growps" Duke Mathematical Journal. (発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] T. Umeda: "Another look at the differential operators" Osaka Journal of Mathematics. (発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] H. Hijikata: "Bass orders in non semisimple algebras" Journal of Mathmatics of Kyoto University. 34. 797-837 (1994)

    • Related Report
      1995 Annual Research Report
  • [Publications] Hiroyuki Yoshida: "On the zeta function of Shimura varieties and periods of Hilbert modular forms" Duke Mathematical Journal. 75. 121-191 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Hiroyuki Yoshida: "On a conjecture of Shimura concerning periods of Hilbert modular forms" American Journal of Mathematics. (発売予定).

    • Related Report
      1994 Annual Research Report
  • [Publications] Hiroaki HIjikata: "Bass orders in non semisimple algebras" Journal of Mathematics of Kyoto University. 34. 797-837 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Tamotsu Ikeda: "On the theory of Jacobi forms and Fourier-Jacobi coefficients of Eisenstem serie" Journal of Mathematics of Kyoto University. 34. 615-636 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Takeshi Hirai: "Representations of Diffeomorphism groups and the intinite symmetric group" Noncompact Lie groups and some of their applications(Kluwer). 225-237 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Toru Umeda(with Nogchi and Wakayama): "A quantum analogue of the Capelli identity and an elementary calculns on GLq(72)" Duke Mathematical Journal. 76. 567-594 (1994)

    • Related Report
      1994 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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