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L-functions attached to non-holomorphic Siegel modular forms-Local theory and its global applications

Research Project

Project/Area Number 20740015
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionOsaka University

Principal Investigator

MORIYAMA Tomonori  大阪大学, 大学院・理学研究科, 准教授 (80384171)

Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords保型的L関数 / Fourier展開 / 整数論 / 保型形式 / L関数 / フーリエ展開 / 局所理論 / プーリエ展開 / Eisenstein級数
Research Abstract

We study the archimedean local theory of Fourier expansion of non-holomorphic Siegel modular forms of degree 2 along the Siegel parabolic subgroup. We established the multiplicity free theorem for generalized Whittaker models(=Bessel models) of GSp(2, R) associated with indefinite binary quadratic forms when they arise from various standard representations. We also obtained an explicit integral expression of the corresponding generalized Whittaker functions on a one dimensional torus of GSp(2, R).

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (38 results)

All 2012 2011 2010 2009 2008 Other

All Journal Article (15 results) (of which Peer Reviewed: 6 results) Presentation (22 results) Remarks (1 results)

  • [Journal Article] Generalized Whittaker functions on GSp(2, R) associated with indefinite quadratic forms2011

    • Author(s)
      Tomonori Moriyama
    • Journal Title

      Journal of the Mathematical society of Japan

      Volume: 63

    • NAID

      10030344828

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 保型形式の空間とHecke作用素2011

    • Author(s)
      森山知則
    • Journal Title

      第18回(2010年度)整数論サマースクール「アーサー・セルバーグ跡公式入門」報告集

    • Related Report
      2011 Final Research Report
  • [Journal Article] Generalized Whittaker functions on <i>GSp</i>(2,<i><b>R</b></i>) associated with indefinite quadratic forms2011

    • Author(s)
      Tomonori Moriyama
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 63 Issue: 4 Pages: 1203-1262

    • DOI

      10.2969/jmsj/06341203

    • NAID

      10030344828

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 保型形式の空間とHecke作用素2011

    • Author(s)
      森山知則
    • Journal Title

      第18回整数論サマースクール「アーサー・セルバーグ跡公式入門」報告集

      Pages: 1-20

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] 保型形式の空間とHecke作用素2011

    • Author(s)
      森山知則
    • Journal Title

      第18回整数論サマースクール報告集

      Pages: 1-20

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Uniqueness of generalized Whittaker models for GSp(2, R) and the outer automorphism group of Sp(2, R)2010

    • Author(s)
      石井卓, 森山知則
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1715 Pages: 121-126

    • Related Report
      2011 Final Research Report
  • [Journal Article] Uniqueness of generalized Whittakermodels for GSp(2, R)$and the outerautomorphism group of Sp(2, R)2010

    • Author(s)
      石井卓, 森山知則
    • Journal Title

      数理解析研究所講究録 1715

      Pages: 121-126

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] Uniqueness of generalized Whittaker models for GSp(2, R) and the outer automorphism group of Sp(2, R)2010

    • Author(s)
      石井卓, 森山知則
    • Journal Title

      数理解析研究所講究録

      Volume: 1715 Pages: 121-126

    • Related Report
      2010 Annual Research Report
  • [Journal Article] L-functionsfor GSp(2)×GL(2): Archimedean theory and applications2009

    • Author(s)
      Tomonori Moriyama
    • Journal Title

      Canadian Journal of Mathematics

      Volume: 61 Pages: 395-426

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Langlands-Shahidi method概説2009

    • Author(s)
      森山知則
    • Journal Title

      第16回(2008年度)整数論サマースクール「保型L関数」報告集

      Pages: 225-248

    • Related Report
      2011 Final Research Report
  • [Journal Article] Langlands-Shahidi method概説2009

    • Author(s)
      森山知則
    • Journal Title

      第16回整数論サマースクール「保型L関数」報告集

      Pages: 225-228

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] L-functions for GSp(2) × GL(2) : archimedean theory and applications2009

    • Author(s)
      Tomonori Moriyama
    • Journal Title

      Canadian Journal of Mathematics 61

      Pages: 395-426

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spinor L-functions for generic cusp forms on GSp(2) belonging to principal series representations2008

    • Author(s)
      Taku Ishii, Tomonori Moriyama
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: 360

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spinor L-functions for generic cusp forms on GSp (2) belonging to principal series representations2008

    • Author(s)
      Taku Ishii and Tomonori Moriyama
    • Journal Title

      Transactions of the American Mathematical Society 360

      Pages: 5683-5709

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized Whittaker functions onGSp(2, R) associated with indefinitequadratic forms

    • Author(s)
      森山知則
    • Journal Title

      Journal of theMathematical society of Japan

    • Related Report
      2010 Self-evaluation Report
  • [Presentation] A Fuchsian differential equation with accessory parameters and Zuckemann's tensoring2012

    • Author(s)
      森山知則
    • Organizer
      Branching Laws
    • Place of Presentation
      シンガポール国立大学(シンガポール)
    • Year and Date
      2012-03-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] p進Poisson変換による球関数の構成2012

    • Author(s)
      森山知則
    • Organizer
      p進代数群の表現論
    • Place of Presentation
      横浜国立大学(神奈川県)
    • Year and Date
      2012-02-17
    • Related Report
      2011 Final Research Report
  • [Presentation] p進Poisson変換による球関数の構成2012

    • Author(s)
      森山知則
    • Organizer
      p進代数群の表現論
    • Place of Presentation
      横浜国立大学(神奈川県)(招待講演)
    • Year and Date
      2012-02-17
    • Related Report
      2011 Annual Research Report
  • [Presentation] 保型形式の空間とHecke作用素2010

    • Author(s)
      森山知則
    • Organizer
      第18回(2010年度)整数論サマースクール「アーサー・セルバーグ跡公式入門」
    • Place of Presentation
      山中温泉河鹿荘ロイヤルホテル(石川県)
    • Year and Date
      2010-09-06
    • Related Report
      2011 Final Research Report
  • [Presentation] 保型形式の空間とHecke作用素2010

    • Author(s)
      森山知則
    • Organizer
      第18回整数論サマースクール
    • Place of Presentation
      山中温泉河鹿荘ロイヤルホテル(石川県)(招待講演)
    • Year and Date
      2010-09-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] Kohnen-Skoruppaの論文(Invent Math, 1988)の紹介」2010

    • Author(s)
      森山知則
    • Organizer
      GSp(4)の数論を中心とした基礎的ワークショップ
    • Place of Presentation
      大阪大学大学院理学研究科
    • Year and Date
      2010-08-04
    • Related Report
      2011 Final Research Report
  • [Presentation] Kohnen-Skoruppaの論文(Invent math 1988)の紹介2010

    • Author(s)
      森山知則
    • Organizer
      GSp(4)の数論を中心とした基礎的ワークショップ
    • Place of Presentation
      大阪大学大学院理学研究科(大阪府)(招待講演)
    • Year and Date
      2010-08-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] GSp(4)からGL(4)へのgeneric transferの解説2010

    • Author(s)
      森山知則
    • Organizer
      GSp(4)の数論を中心とした基礎的ワークショップ
    • Place of Presentation
      大阪大学大学院理学研究科
    • Year and Date
      2010-08-03
    • Related Report
      2011 Final Research Report
  • [Presentation] GSp(4)からGL(4)へのgeneric transferの解説2010

    • Author(s)
      森山知則
    • Organizer
      GSp(4)の数論を中心とした基礎的ワークショップ
    • Place of Presentation
      大阪大学大学院理学研究科(大阪府)(招待講演)
    • Year and Date
      2010-08-03
    • Related Report
      2010 Annual Research Report
  • [Presentation] 実解析的Siegel保型形式のFourier展開と保型的L関数2010

    • Author(s)
      森山知則
    • Organizer
      大阪市立大学数学談話会
    • Place of Presentation
      大阪市立大学大学院理学研究科
    • Year and Date
      2010-06-03
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] A Fuchsian differential equations with accessory parameters and Zuckermann' s tensoring, Blanching Laws2010

    • Author(s)
      森山知則
    • Organizer
      Institute for Mathematical Sciences, National University of Singapore
    • Place of Presentation
      シンガポール
    • Year and Date
      2010-03-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Uniqueness of generalized Whittaker models for GSp(2, R) and the outer automorphism group of Sp(2, R)2010

    • Author(s)
      石井卓, 森山知則
    • Organizer
      保型形式・保型表現およびそれに伴うL函数と周期の研究(RIMS研究集会)
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2010-01-20
    • Related Report
      2011 Final Research Report
  • [Presentation] Uniqueness of generalized Whittakermodels for GSp(2, R)and the outerautomorphism group of Sp(2, R)2010

    • Author(s)
      石井卓, 森山知則
    • Organizer
      「保型形式・保型表現およびそれに伴うL函数と周期の研究」(RIMS研究集会)
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2010-01-20
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Uniqueness of generalized Whittaker models for GSp(2,R) and the outer automorphism group of Sp(2,R)2010

    • Author(s)
      石井卓, 森山知則
    • Organizer
      保型形式・保型表現およびそれに伴うL函数と周期の研究
    • Place of Presentation
      東大大学数理科学研究科
    • Year and Date
      2010-01-20
    • Related Report
      2009 Annual Research Report
  • [Presentation] Real local counterpart ; Problems and Speculations II2009

    • Author(s)
      森山知則
    • Organizer
      ワークショップ保型表現の分岐理論へ向けて:ε-因子の明示計算
    • Place of Presentation
      京都大学大学院理学研究科
    • Year and Date
      2009-08-13
    • Related Report
      2011 Final Research Report
  • [Presentation] Real local counterpart ; Problems and Speculations II2009

    • Author(s)
      森山知則
    • Organizer
      ワークショップ 保型表現の分岐理論へ向けて : ε-因子の明示計算
    • Place of Presentation
      京都大学理学研究科
    • Year and Date
      2009-08-13
    • Related Report
      2009 Annual Research Report
  • [Presentation] Construction of supercuspidals : prime N case2009

    • Author(s)
      森山知則
    • Organizer
      ワークショップ保型表現の分岐理論へ向けて:ε-因子の明示計算
    • Place of Presentation
      京都大学大学院理学研究科
    • Year and Date
      2009-08-10
    • Related Report
      2011 Final Research Report
  • [Presentation] Construction of supercuspidals : prime N case2009

    • Author(s)
      森山知則
    • Organizer
      ワークショップ 保型表現の分岐理論へ向けて : ε-因子の明示計算
    • Place of Presentation
      京都大学理学研究科
    • Year and Date
      2009-08-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] 2次実解析的Siegel保型形式とそのL関数2009

    • Author(s)
      森山知則
    • Organizer
      東北大学代数セミナー
    • Place of Presentation
      東北大学大学院理学研究科
    • Year and Date
      2009-06-25
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report 2009 Annual Research Report
  • [Presentation] Langlands-Shahidi method概説2008

    • Author(s)
      森山知則
    • Organizer
      第16回整数論サマースクール「保型L関数」
    • Place of Presentation
      幕張メッセ(千葉県)
    • Year and Date
      2008-08-20
    • Related Report
      2011 Final Research Report
  • [Presentation] Langlands-Shahidi method概説2008

    • Author(s)
      森山知則
    • Organizer
      第16回整数論サマースクール「保型L関数」
    • Place of Presentation
      幕張メッセ
    • Year and Date
      2008-08-20
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Langlands-Shahidi method概説2008

    • Author(s)
      森山知則
    • Organizer
      第16回整数論サマースクール
    • Place of Presentation
      幕張メッセ
    • Year and Date
      2008-08-20
    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.sci.osaka-u.ac.jp/~moriyama/

    • Related Report
      2011 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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