Special values of automorphic L-functions and periods

• Project/Area Number: 26800017
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Kyoto 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: ¥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)
• Keywords: L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.

Research Products

• [Int'l Joint Research] 台湾国立大学(台湾)
• [Int'l Joint Research] POSTECH(韓国)
• [Journal Article] Endoscopic A-packets for unitary groups (2018)
  • Author(s): 山名俊介
  • Journal Title: 数理解析研究所考究録 Volume: 印刷中
• [Journal Article] Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences (2018)
  • Author(s): Sungman Cho, Shunsuke Yamana, Takuya Yamauchi
  • Journal Title: MPIM Preprint Collection Volume: 15 Pages: 1-23
  • Int'l Joint Research
• [Journal Article] Bessel periods and anticyclotomic p-adic spinor L-functions (2018)
  • Author(s): Ming-Lun Hsieh, Shunsuke Yamana
  • Journal Title: MPIM Preprint Collection Volume: 16 Pages: 1-57
  • Int'l Joint Research
• [Journal Article] Local symmetric square L-factors of representations of general linear groups (2017)
  • Author(s): Shunsuke Yamana
  • Journal Title: Pacific Journal of Mathematics Volume: 286 Issue: 1 Pages: 215-256
  • DOI: 10.2140/pjm.2017.286.215
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Siegel series for skew Hermitian forms over quaternion algebras (2017)
  • 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
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Twisted symmetric square L-functions and invariant trilinear forms (2017)
  • 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
  • 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
  • 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
  • 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
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Periods of automorphic forms: the trilinear case (2016)
  • 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
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On the lifting of Hilbert cusp forms (2016)
  • Author(s): 山名俊介
  • Journal Title: 数理解析研究所講究録 Volume: in press
  • 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
  • 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
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Periods of residual automorphic forms (2015)
  • 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
  • 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
  • Acknowledgement Compliant
• [Presentation] Bocherer conjecture and anticyclotomic p-adic spinor L-functions (2018)
  • Author(s): 山名俊介
  • Organizer: セミナー (Mannheim University)
• [Presentation] Bessel periods and anticyclotomic p-adic spinor L-functions (2018)
  • Author(s): 山名俊介
  • Organizer: セミナー (Max Planck Institute for Mathematics)
• [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
  • Int'l Joint Research / Invited
• [Presentation] Derivative of Eisenstein series of weight 2 and intersection numbers (2017)
  • Author(s): 山名俊介
  • Organizer: Special values of automorphic L-functions, periods of automorphic forms and related topics
  • Invited
• [Presentation] On the lifting of Hilbert cups forms to Hilbert Siegel cusp forms (2017)
  • Author(s): 山名俊介
  • Organizer: セミナー (the Aachen University)
• [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)
• [Presentation] Derivative of Eisenstein series of weight 2 and intersection numbers (2017)
  • Author(s): 山名俊介
  • Organizer: セミナー (KIAS)
• [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)
• [Presentation] On the lifting of Hilbert cups forms (2017)
  • Author(s): 山名俊介
  • Organizer: セミナー (Purdue University)
• [Presentation] Derivative of Eisenstein series of weight 2 and intersection numbers (2017)
  • Author(s): 山名俊介
  • Organizer: セミナー (University of Toronto)
• [Presentation] Derivative of Eisenstein series of weight 2 and intersection numbers (2017)
  • Author(s): 山名俊介
  • Organizer: セミナー (University of Heidelberg)
• [Presentation] Endoscopic A-packets for unitary groups (2017)
  • 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
• [Presentation] Modular forms and representation numbers (2017)
  • Author(s): 山名俊介
  • Organizer: The 2nd KGTU Mathematics Research Workshop for Young Researchers
  • Place of Presentation: 京都大学
  • Invited
• [Presentation] he number of representations of a symmetric matrix by a quadratic form (2017)
  • 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
• [Presentation] The global theta correspondence and Rallis’ inner product formula (2017)
  • Author(s): 山名俊介
  • Organizer: Hodge conjecture on Unitary Shimura Varieties and Aq(λ)
  • Place of Presentation: 岡山大学
  • Invited
• [Presentation] On the lifting of Hilbert cusp forms (2016)
  • 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
  • Invited
• [Presentation] On the lifting of Hilbert cusp forms (2016)
  • 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
  • Int'l Joint Research
• [Presentation] On the lifting of Hilbert cusp forms to holomorphic cusp forms on quaternionic unitary groups (2016)
  • 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
  • Invited
• [Presentation] On the lifting of Hilbert cusp forms to Hilbert-Siegel cusp forms (2016)
  • 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
  • Int'l Joint Research
• [Presentation] On the lifting of Hilbert cusp forms to Hilbert-Hermitian cusp forms (2016)
  • 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
  • Int'l Joint Research
• [Presentation] On the lifting of Hilbert cusp forms to Hilbert-Siegel cusp forms (2016)
  • 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)
  • Int'l Joint Research / Invited
• [Presentation] On certain families of CAP representations for metaplectic and orthogonal groups (2016)
  • Author(s): 山名俊介
  • Organizer: Automorphic Forms on Metaplectic Forms and Related Topics
  • Place of Presentation: インド(Pune)
  • Int'l Joint Research / Invited
• [Presentation] On the lifting of Hilbert cusp forms (2016)
  • 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)
  • Int'l Joint Research
• [Presentation] CAP representations indexed by Hilbert cusp forms (2016)
  • Author(s): 山名俊介
  • Organizer: Japan-Taiwan Joint Conference on Number Theory 2016
  • Place of Presentation: 台湾(台北)
  • Int'l Joint Research / Invited
• [Presentation] The CAP representations indexed by Hilbert cusp forms (2016)
  • 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)
• [Presentation] On the lifting of Hilbert cusp forms to Hilbert-Siegel cusp forms (2016)
  • 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)
• [Presentation] Modular forms from classical to modern (2016)
  • Author(s): 山名俊介
  • Organizer: 談話会(National Technical University of Athens)
  • Place of Presentation: ギリシャ(Athens)
• [Presentation] CAP representations indexed by Hilbert cusp forms (2016)
  • Author(s): 山名俊介
  • Organizer: セミナー(Morningside Center of Mathematics)
  • Place of Presentation: 中国(Beijing)
• [Presentation] Siegel series for skew Hermitian forms over quaternion algebras (2015)
  • 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
• [Presentation] A lifting of Hilbert cusp forms to Hilbert-Siegel cusp forms (2015)
  • 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
• [Presentation] On the lifting of Hilbert cusp forms to holomorphic cusp forms on quaternionic unitary groups (2015)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Gan-Gross-Prasad conjecture for metaplectic groups (2015)
  • 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
• [Presentation] Periods of residual automorphic forms (2015)
  • Author(s): 山名俊介
  • Organizer: 談話会
  • Place of Presentation: 京都大学
  • Year and Date: 2015-06-03
• [Presentation] Local symmetric square L-functions and invariant trilinear forms (2015)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Periods of residual automorphic forms (2015)
  • 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
• [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
  • Invited
• [Presentation] Local symmetric square L-factors and invariant trilinear forms (2015)
  • 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
• [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
• [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
  • Invited
• [Presentation] Symmetric square L-functions of GL(n) and invariant trilinear forms (2014)
  • Author(s): 山名俊介
  • Organizer: CIRM Number Theory Seminar
  • Place of Presentation: CIRM
  • Year and Date: 2014-09-09
  • 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
• [Presentation] Symmetric square L-functions of GL(n) and invariant trilinear forms (2014)
  • 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
• [Presentation] L-functions and theta correspondence (2014)
  • 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
• [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
  • Invited
• [Presentation] Periods of residual automorphic forms (2014)
  • 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
  • Invited
• [Presentation] Periods of residual automorphic forms (2014)
  • 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
  • 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
• [Presentation] Periods of residual automorphic forms (2014)
  • 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
  • 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
  • Invited
• [Remarks] Shunsuke Yamana Home Page
  • URL: http://syamana.sub.jp
• [Remarks] Shunsuke Yamana Home Page
  • URL: http://syamana.sub.jp/