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Special values of automorphic L-functions and periods

Research Project

Project/Area Number 26800017
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionKyoto University (2015-2017)
Kyushu University (2014)

Principal Investigator

Yamana Shunsuke  京都大学, 白眉センター, 特定助教 (50633301)

Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
KeywordsL関数 / ヒルベルトモジュラー形式 / ジーゲルモジュラー形式 / 周期 / 池田リフティング / アイゼンシュタイン級数 / 格別表現 / テータ対応 / p進L関数 / j関数 / 志村多様体 / Boecherer予想 / リフティング / モジュライスタック / テータリフト / 退化主系列表現 / 交点数 / 池田リフト / 斎藤-黒川リフト / Kudlaリフト / Arthur予想 / ヒルベルト保型形式 / ジーゲル保型形式 / エルミート保型形式 / ジーゲル級数 / 志村対応 / ジャッケ積分 / 二次対称積L関数 / 二次対称積L因子 / Rankin-Selberg法 / 例外表現 / 二重被覆群 / 三重積周期 / Whittaker模型
Outline of Final Research Achievements

I developed a local theory of twisted symmetric square L-factors of representations of general linear groups and characterized its pole in terms of distinction by exceptional representations. I constructed Hilbert-Siegel cusp forms and Hilbert-Hermite cusp forms explicitly by generalizing Ikeda's construction of a lifting of elliptic cusp forms to a lifting of Hilbert cusp forms, and applied it to the basis problem and the theory of quadratic forms.
I constructed anti-cyclotomic p-adic spinor L-functions of paramodular Siegel cusp forms of degree 2 by using the Bessel period.
I computed Fourier coefficients of the non-central derivative of degree 4 Siegel Eisenstein series and relate it to the central derivative of degree 3 Siegel Eisenstein series.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (68 results)

All 2018 2017 2016 2015 2014 Other

All Int'l Joint Research (2 results) Journal Article (15 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 7 results,  Acknowledgement Compliant: 12 results) Presentation (49 results) (of which Int'l Joint Research: 10 results,  Invited: 19 results) Remarks (2 results)

  • [Int'l Joint Research] 台湾国立大学(台湾)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] POSTECH(韓国)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Endoscopic A-packets for unitary groups2018

    • Author(s)
      山名俊介
    • Journal Title

      数理解析研究所考究録

      Volume: 印刷中

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences2018

    • Author(s)
      Sungman Cho, Shunsuke Yamana, Takuya Yamauchi
    • Journal Title

      MPIM Preprint Collection

      Volume: 15 Pages: 1-23

    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Journal Article] Bessel periods and anticyclotomic p-adic spinor L-functions2018

    • Author(s)
      Ming-Lun Hsieh, Shunsuke Yamana
    • Journal Title

      MPIM Preprint Collection

      Volume: 16 Pages: 1-57

    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Journal Article] Local symmetric square L-factors of representations of general linear groups2017

    • Author(s)
      Shunsuke Yamana
    • Journal Title

      Pacific Journal of Mathematics

      Volume: 286 Issue: 1 Pages: 215-256

    • DOI

      10.2140/pjm.2017.286.215

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Siegel series for skew Hermitian forms over quaternion algebras2017

    • Author(s)
      Shunsuke Yamana
    • Journal Title

      Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

      Volume: 87 Issue: 1 Pages: 43-59

    • DOI

      10.1007/s12188-016-0127-4

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Twisted symmetric square L-functions and invariant trilinear forms2017

    • Author(s)
      Eyal Kaplan, Shunsuke Yamana
    • Journal Title

      Mathematische Zeitschrift

      Volume: 285 Issue: 3-4 Pages: 739-793

    • DOI

      10.1007/s00209-016-1726-6

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] ヒルベルト形式からヒルベルト-ジーゲル形式へのリフティング2017

    • Author(s)
      山名俊介
    • Journal Title

      数理解析研究所考究録

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] ヒルベルト形式からヒルベルト-エルミート形式へのリフティング2017

    • Author(s)
      山名俊介
    • Journal Title

      早稲田大学整数論研究集会2016報告集

      Volume: 20 Pages: 6-22

    • Related Report
      2016 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] Periods of automorphic forms: the case of (U(n+1)×U(n), U(n))2016

    • Author(s)
      山名俊介, 市野篤史
    • Journal Title

      Journal fur die reine und angewandte Mathematik

      Volume: in press

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Periods of automorphic forms: the trilinear case2016

    • Author(s)
      山名俊介
    • Journal Title

      Journal of the Institute of Mathematics Jussieu

      Volume: in press Issue: 1 Pages: 59-74

    • DOI

      10.1017/s1474748015000377

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On the lifting of Hilbert cusp forms2016

    • Author(s)
      山名俊介
    • Journal Title

      数理解析研究所講究録

      Volume: in press

    • Related Report
      2015 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] ヒルベルト保型形式のリフティング2016

    • Author(s)
      山名俊介
    • Journal Title

      2016年早稲田整数論研究集会報告集

      Volume: in press

    • Related Report
      2015 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] On poles of the exterior cube L-functions of GL(6)2015

    • Author(s)
      山名俊介
    • Journal Title

      Mathematische Zeitschrift

      Volume: 279 Issue: 1-2 Pages: 267-270

    • DOI

      10.1007/s00209-014-1366-7

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Periods of residual automorphic forms2015

    • Author(s)
      山名俊介
    • Journal Title

      Journal of Functional Analysis

      Volume: 268 Issue: 5 Pages: 1078-1104

    • DOI

      10.1016/j.jfa.2014.11.009

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] 局所二次対称積$L$函数と三重線形形式2015

    • Author(s)
      山名俊介
    • Journal Title

      数理解析研究所考究録

      Volume: in press

    • Related Report
      2014 Research-status Report
    • Acknowledgement Compliant
  • [Presentation] Bocherer conjecture and anticyclotomic p-adic spinor L-functions2018

    • Author(s)
      山名俊介
    • Organizer
      セミナー (Mannheim University)
    • Related Report
      2017 Annual Research Report
  • [Presentation] Bessel periods and anticyclotomic p-adic spinor L-functions2018

    • Author(s)
      山名俊介
    • Organizer
      セミナー (Max Planck Institute for Mathematics)
    • Related Report
      2017 Annual Research Report
  • [Presentation] On the lifting of endoscopic cusp forms on U(3) to cusp forms on U(4m+ 3)2017

    • Author(s)
      山名俊介
    • Organizer
      New directions in automorphic forms and L-functions
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Derivative of Eisenstein series of weight 2 and intersection numbers2017

    • Author(s)
      山名俊介
    • Organizer
      Special values of automorphic L-functions, periods of automorphic forms and related topics
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] On the lifting of Hilbert cups forms to Hilbert Siegel cusp forms2017

    • Author(s)
      山名俊介
    • Organizer
      セミナー (the Aachen University)
    • Related Report
      2017 Annual Research Report
  • [Presentation] On the lifting of endoscopic cusp forms on U(3) to cusp forms on U(4m+ 3)2017

    • Author(s)
      山名俊介
    • Organizer
      セミナー (the Academia Sinica)
    • Related Report
      2017 Annual Research Report
  • [Presentation] Derivative of Eisenstein series of weight 2 and intersection numbers2017

    • Author(s)
      山名俊介
    • Organizer
      セミナー (KIAS)
    • Related Report
      2017 Annual Research Report
  • [Presentation] On the lifting of endoscopic cusp forms on U(3) to cusp forms on U(4m+ 3)2017

    • Author(s)
      山名俊介
    • Organizer
      セミナー (KIAS)
    • Related Report
      2017 Annual Research Report
  • [Presentation] On the lifting of Hilbert cups forms2017

    • Author(s)
      山名俊介
    • Organizer
      セミナー (Purdue University)
    • Related Report
      2017 Annual Research Report
  • [Presentation] Derivative of Eisenstein series of weight 2 and intersection numbers2017

    • Author(s)
      山名俊介
    • Organizer
      セミナー (University of Toronto)
    • Related Report
      2017 Annual Research Report
  • [Presentation] Derivative of Eisenstein series of weight 2 and intersection numbers2017

    • Author(s)
      山名俊介
    • Organizer
      セミナー (University of Heidelberg)
    • Related Report
      2017 Annual Research Report
  • [Presentation] Endoscopic A-packets for unitary groups2017

    • Author(s)
      山名俊介
    • Organizer
      RIMS研究集会「保型形式とその周辺」
    • Place of Presentation
      京都大学
    • Related Report
      2016 Research-status Report
  • [Presentation] Modular forms and representation numbers2017

    • Author(s)
      山名俊介
    • Organizer
      The 2nd KGTU Mathematics Research Workshop for Young Researchers
    • Place of Presentation
      京都大学
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] he number of representations of a symmetric matrix by a quadratic form2017

    • Author(s)
      山名俊介
    • Organizer
      第10回ゼータ若手研究集会
    • Place of Presentation
      名古屋大学
    • Related Report
      2016 Research-status Report
  • [Presentation] The global theta correspondence and Rallis’ inner product formula2017

    • Author(s)
      山名俊介
    • Organizer
      Hodge conjecture on Unitary Shimura Varieties and Aq(λ)
    • Place of Presentation
      岡山大学
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] On the lifting of Hilbert cusp forms2016

    • Author(s)
      山名俊介
    • Organizer
      早稲田大学整数論研究集会2016
    • Place of Presentation
      早稲田大学西早稲田キャンパス
    • Year and Date
      2016-03-21
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] On the lifting of Hilbert cusp forms2016

    • Author(s)
      山名俊介
    • Organizer
      International Workshop: New Developments in Representation Theory
    • Place of Presentation
      National University of Singapore
    • Year and Date
      2016-03-15
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] On the lifting of Hilbert cusp forms to holomorphic cusp forms on quaternionic unitary groups2016

    • Author(s)
      山名俊介
    • Organizer
      南大阪保型表現セミナー
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2016-02-12
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] On the lifting of Hilbert cusp forms to Hilbert-Siegel cusp forms2016

    • Author(s)
      山名俊介
    • Organizer
      RIMS研究集会「保型形式、保型的L関数とその周辺」
    • Place of Presentation
      京都大学
    • Year and Date
      2016-02-04
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] On the lifting of Hilbert cusp forms to Hilbert-Hermitian cusp forms2016

    • Author(s)
      山名俊介
    • Organizer
      RIMS研究集会「保型形式、保型的L関数とその周辺」
    • Place of Presentation
      京都大学
    • Year and Date
      2016-02-04
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] On the lifting of Hilbert cusp forms to Hilbert-Siegel cusp forms2016

    • Author(s)
      山名俊介
    • Organizer
      Relative Trace Formula, Periods, L-Functions, Harmonic Analysis and Langlands Functoriality
    • Place of Presentation
      フランス(Luminy)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On certain families of CAP representations for metaplectic and orthogonal groups2016

    • Author(s)
      山名俊介
    • Organizer
      Automorphic Forms on Metaplectic Forms and Related Topics
    • Place of Presentation
      インド(Pune)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the lifting of Hilbert cusp forms2016

    • Author(s)
      山名俊介
    • Organizer
      Building Bridges: 3rd EU/US Summer School + Workshop on Automorphic Forms and Related Topics
    • Place of Presentation
      ボスニア・ヘルツェゴビナ(Sarajevo)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] CAP representations indexed by Hilbert cusp forms2016

    • Author(s)
      山名俊介
    • Organizer
      Japan-Taiwan Joint Conference on Number Theory 2016
    • Place of Presentation
      台湾(台北)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The CAP representations indexed by Hilbert cusp forms2016

    • Author(s)
      山名俊介
    • Organizer
      19th Autumn Workshop on Number Theory, Archimedean local theory of automorphic forms
    • Place of Presentation
      白馬ハイマウントホテル(長野)
    • Related Report
      2016 Research-status Report
  • [Presentation] On the lifting of Hilbert cusp forms to Hilbert-Siegel cusp forms2016

    • Author(s)
      山名俊介
    • Organizer
      セミナー(The State University of New Jersey)
    • Place of Presentation
      アメリカ合衆国(Newark)
    • Related Report
      2016 Research-status Report
  • [Presentation] Modular forms from classical to modern2016

    • Author(s)
      山名俊介
    • Organizer
      談話会(National Technical University of Athens)
    • Place of Presentation
      ギリシャ(Athens)
    • Related Report
      2016 Research-status Report
  • [Presentation] CAP representations indexed by Hilbert cusp forms2016

    • Author(s)
      山名俊介
    • Organizer
      セミナー(Morningside Center of Mathematics)
    • Place of Presentation
      中国(Beijing)
    • Related Report
      2016 Research-status Report
  • [Presentation] Siegel series for skew Hermitian forms over quaternion algebras2015

    • Author(s)
      山名俊介
    • Organizer
      大阪大学保型形式セミナー,
    • Place of Presentation
      大阪大学
    • Year and Date
      2015-11-13
    • Related Report
      2015 Research-status Report
  • [Presentation] A lifting of Hilbert cusp forms to Hilbert-Siegel cusp forms2015

    • Author(s)
      山名俊介
    • Organizer
      Workshop on Automorphic Forms and Representations
    • Place of Presentation
      University of Rijeka, Croatia
    • Year and Date
      2015-09-23
    • Related Report
      2015 Research-status Report
  • [Presentation] On the lifting of Hilbert cusp forms to holomorphic cusp forms on quaternionic unitary groups2015

    • Author(s)
      山名俊介
    • Organizer
      East Asia Number Theory Conference (EANTC 2015)
    • Place of Presentation
      Elysian Ganchon, Chunchen, Korea
    • Year and Date
      2015-08-25
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Gan-Gross-Prasad conjecture for metaplectic groups2015

    • Author(s)
      山名俊介
    • Organizer
      第三回京都保型形式研究集会
    • Place of Presentation
      京都大学
    • Year and Date
      2015-06-26
    • Related Report
      2015 Research-status Report
  • [Presentation] Periods of residual automorphic forms2015

    • Author(s)
      山名俊介
    • Organizer
      談話会
    • Place of Presentation
      京都大学
    • Year and Date
      2015-06-03
    • Related Report
      2015 Research-status Report
  • [Presentation] Local symmetric square L-functions and invariant trilinear forms2015

    • Author(s)
      山名俊介
    • Organizer
      Representation theory and number theory workshop
    • Place of Presentation
      National University of Singapore
    • Year and Date
      2015-04-20
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Periods of residual automorphic forms2015

    • Author(s)
      山名俊介
    • Organizer
      九大代数学セミナー
    • Place of Presentation
      九州大学
    • Year and Date
      2015-03-27
    • Related Report
      2014 Research-status Report
  • [Presentation] GL(6)の三重交代積L関数,2015

    • Author(s)
      山名俊介
    • Organizer
      日本数学会2015年度代数学分科会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-24
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Local symmetric square L-factors and invariant trilinear forms2015

    • Author(s)
      山名俊介
    • Organizer
      オハイオ州立大学整数論セミナー
    • Place of Presentation
      Ohio State University
    • Year and Date
      2015-03-11
    • Related Report
      2014 Research-status Report
  • [Presentation] 局所二次対称積$L$関数と三重線形形式2015

    • Author(s)
      山名俊介
    • Organizer
      RIMS研究集会
    • Place of Presentation
      京都大学
    • Year and Date
      2015-02-04
    • Related Report
      2014 Research-status Report
  • [Presentation] Poles of twisted exterior cube L-functions for GL(6)2014

    • Author(s)
      山名俊介
    • Organizer
      日韓整数論セミナー
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2014-11-21
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Symmetric square L-functions of GL(n) and invariant trilinear forms2014

    • Author(s)
      山名俊介
    • Organizer
      CIRM Number Theory Seminar
    • Place of Presentation
      CIRM
    • Year and Date
      2014-09-09
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Poles of twisted exterior cube L-functions for GL(6)2014

    • Author(s)
      山名俊介
    • Organizer
      リエカ大学整数論セミナー
    • Place of Presentation
      University of Rijeka
    • Year and Date
      2014-09-05
    • Related Report
      2014 Research-status Report
  • [Presentation] Symmetric square L-functions of GL(n) and invariant trilinear forms2014

    • Author(s)
      山名俊介
    • Organizer
      ザグレブ大学整数論セミナー
    • Place of Presentation
      University of Zagreb
    • Year and Date
      2014-09-02
    • Related Report
      2014 Research-status Report
  • [Presentation] L-functions and theta correspondence2014

    • Author(s)
      山名俊介
    • Organizer
      ザグレブ大学整数論セミナー
    • Place of Presentation
      University of Zagreb
    • Year and Date
      2014-09-02
    • Related Report
      2014 Research-status Report
  • [Presentation] Poles of twisted exterior cube L-functions for GL(6)2014

    • Author(s)
      山名俊介
    • Organizer
      Building Bridges Workshop on Automorphic Forms and Related Topics
    • Place of Presentation
      University of Bristol
    • Year and Date
      2014-07-09
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Periods of residual automorphic forms2014

    • Author(s)
      山名俊介
    • Organizer
      Summer School in Paris on ``The Gan-Gross-Prasad conjectures''
    • Place of Presentation
      パリ7大学
    • Year and Date
      2014-06-23
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Periods of residual automorphic forms2014

    • Author(s)
      山名俊介
    • Organizer
      Banff workshop on ``The future of trace formulas''
    • Place of Presentation
      バンフセンター
    • Year and Date
      2014-06-05
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Exterior cube L-functions for GL(6)2014

    • Author(s)
      山名俊介
    • Organizer
      マンハイム大学数論セミナー
    • Place of Presentation
      マンハイム大学
    • Year and Date
      2014-05-08
    • Related Report
      2014 Research-status Report
  • [Presentation] Periods of residual automorphic forms2014

    • Author(s)
      山名俊介
    • Organizer
      ハイデルベルク大学数論セミナー
    • Place of Presentation
      ハイデルベルク大学
    • Year and Date
      2014-05-07
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Symmetric square L-functions of GL(n)2014

    • Author(s)
      山名俊介
    • Organizer
      Oberwolfach Workshop, Modular Forms
    • Place of Presentation
      オーベルヴォルヴァッハ数学研究所
    • Year and Date
      2014-04-30
    • Related Report
      2014 Research-status Report
    • Invited
  • [Remarks] Shunsuke Yamana Home Page

    • URL

      http://syamana.sub.jp

    • Related Report
      2017 Annual Research Report
  • [Remarks] Shunsuke Yamana Home Page

    • URL

      http://syamana.sub.jp/

    • Related Report
      2015 Research-status Report

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Published: 2014-04-04   Modified: 2022-08-18  

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