On the special values of the product of L-functions and the periods of automorphic forms defined over function fields

• Project/Area Number: 21654002
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: KONDO Satoshi 東京大学, 数物連携宇宙研究機構, 特任助教 (30372577)
• Co-Investigator(Kenkyū-buntansha): YASUDA Seidai 京都大学, 数理解析研究所, 助教 (90346065)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,280,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥1,100,000 (Direct Cost: ¥1,100,000); Fiscal Year 2009: ¥1,400,000 (Direct Cost: ¥1,400,000)
• Keywords: ドリンフェルト加群 / 保型関数 / 関数体 / L関数の特殊値 / 有限体 / 周期積分 / 代数学

Research Abstract

We verified that when an automorphic form over a function field is integrated over the maximal torus at a fixed prime, the value may be expressed in terms of special values of L-functions, when the function field is that of a projective line over a finite field. We were not able to verify this over the function field of a more general curve.

Research Products

• [Journal Article] Local L and Epsilon factors in Hecke eigenvalues (2012)
  • Author(s): Satoshi Kondo, Seidai Yasuda
  • Journal Title: Journal of Number theory Volume: 132Issue9 Issue: 9 Pages: 1910-1948
  • DOI: 10.1016/j.jnt.2012.03.002
  • Peer Reviewed
• [Journal Article] Local L and epsilon factors in Hecke eigenvalues (2011)
  • Author(s): Satoshi Kondo, Seidai Yasuda
  • Journal Title: J. Pure Appl. Algebra Volume: no.4 Pages: 511-522
• [Journal Article] Zeta elements in the K-theory of Drinfeld modular varieties (2011)
  • Author(s): Satoshi Kondo, Seidai Yasuda
  • Journal Title: に受理済み Volume: 354 Issue: 2 Pages: 529-587
  • DOI: 10.1007/s00208-011-0735-3
  • Peer Reviewed
• [Journal Article] Product structures in motivic cohomology and higher Chow groups (2011)
  • Author(s): Satoshi Kondo, Seidai Yasuda
  • Journal Title: Journal of Pure and Applied Algebra Volume: 215 Pages: 511-522
  • Peer Reviewed
• [Journal Article] On the second rational K-group of an elliptic curve over global fields of positive characteristic (2011)
  • Author(s): Satoshi Kondo, Seidai Yasuda
  • Journal Title: Proceedings of the London Mathematical Society Volume: (掲載確定)
  • Peer Reviewed
• [Presentation] ドリンフェルト加群のモジュライ曲線の有理K2について (2012)
  • Author(s): 近藤智
  • Organizer: 代数幾何とモチーフ理論ワークショップ
  • Place of Presentation: 東北大学(招待講演)
  • Year and Date: 2012-03-09
• [Presentation] Mirahoric representations and the local L-factor (2012)
  • Author(s): Satoshi Kondo
  • Organizer: Workshop "Integrable systems random matrices, algebraic geometry and geometric invariants"
  • Place of Presentation: Steklov Mathematical Instituteモスクワ(ロシア)
  • Year and Date: 2012-02-22
• [Presentation] Mirahoric representations and the local L-factor (2012)
  • Author(s): Satoshi Kondo
  • Organizer: Integrable systems, random matrices, algebraic geometry and geometric invariants
  • Place of Presentation: モスクワ(ロシア)(招待講演)
  • Year and Date: 2012-02-22
• [Presentation] L因子とイプシロン因子 (2012)
  • Author(s): 近藤智
  • Organizer: p進代数群の勉強会
  • Place of Presentation: 横浜国立大学(招待講演)
  • Year and Date: 2012-02-16
• [Presentation] On quasi-generic representations of the general linear group ot a non-archimedean local field (2011)
  • Author(s): 近藤智
  • Organizer: 可積分系、ランダム行列、代数幾何と幾何学的不変量
  • Place of Presentation: 京都大学(招待講演)
  • Year and Date: 2011-10-20
• [Presentation] モチビックホモトピー論での分母なしリーマンロッホの定理について (2011)
  • Author(s): 近藤智
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-29
• [Presentation] Boundary maps to the supersingular points and the evaluation of Drinfeld modular Beilinson-Kato type elements (2011)
  • Author(s): Satoshi Kondo
  • Organizer: The Arithmetic of Function Fields and Related Topics
  • Place of Presentation: 慶州(韓国)(招待講演)
  • Year and Date: 2011-08-19
• [Presentation] On the values of Drinfeld modular Beilinson-Kato type elements at supersingular points (2011)
  • Author(s): Satoshi Kondo
  • Organizer: Workshop on the Arithmetic of Function Fields
  • Place of Presentation: Imperial College London,ロンドン(イギリス)
  • Year and Date: 2011-06-14
• [Presentation] On the values of Drinfeld modular Beilinson-Kato type elements at supersingular points (2011)
  • Author(s): Satoshi Kondo
  • Organizer: Workshop on the Arithmetic of Function Fields
  • Place of Presentation: Imperial College London (UK)(招待講演)
  • Year and Date: 2011-06-14
• [Presentation] Expressions of local L and epsilon factors in Hecke eigenvalues, Workshop on Integrable systems, random matrices (2011)
  • Author(s): Satoshi Kondo
  • Organizer: algebraic geometry and geometric invariants
  • Place of Presentation: Steklov Mathematical Institute,モスクワ(ロシア)
  • Year and Date: 2011-02-09
• [Presentation] Expressions of local L factors and epsilon factors in terms of Hecke eigenvalues (2011)
  • Author(s): 近藤智
  • Organizer: Integrable Systems, Random Matrices, Algebraic Geometry and Geometric Invariants
  • Place of Presentation: ステクロフ高等研究所、モスクワ、ロシア(招待)
  • Year and Date: 2011-02-09
• [Presentation] 局所L因子およびイプシロン因子のヘッケ固有値による表示 (2010)
  • Author(s): 近藤智
  • Organizer: 可積分系、ランダム行列、代数幾何と幾何学的不変量
  • Place of Presentation: 京都大学
  • Year and Date: 2010-12-16
• [Presentation] 局所L因子とイプシロン因子のヘッケ固有値による表示 (2010)
  • Author(s): 近藤智
  • Organizer: L関数の特殊値と数論幾何
  • Place of Presentation: 美山町自然文化村河鹿荘・会議室(招待)
  • Year and Date: 2010-10-08
• [Presentation] アンダーソンによるテータとタウのレビュー (2010)
  • Author(s): 近藤智
  • Organizer: p進佐藤理論と数論幾何
  • Place of Presentation: 東北大学
  • Year and Date: 2010-09-29
• [Presentation] アンダーソンによるテータとタウのレビューI、II (2010)
  • Author(s): 近藤智
  • Organizer: P進佐藤理論と数論幾何
  • Place of Presentation: 東北大学(招待)
  • Year and Date: 2010-09-29
• [Presentation] モティヴィックコホモロジーと高次チャウ群の積構造の互換性 (2010)
  • Author(s): 近藤智
  • Organizer: 2010年秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-24
• [Presentation] モチビックコホモロジーの積構造について (2010)
  • Author(s): 近藤智
  • Organizer: Workshop on arithmetic geometry 2010
  • Place of Presentation: 沖縄尚学高等学校(招待)
  • Year and Date: 2010-08-06
• [Presentation] Part I : First introduction to number theory, Part 2 : Algebraic varieties (schemes) and some conjectures in number theory (2010)
  • Author(s): 近藤智
  • Organizer: IPMU colloquium
  • Place of Presentation: 東京大学数物連携宇宙研究機構
  • Year and Date: 2010-05-19
• [Presentation] On the rational K-group of an elliptic surface over a finite field (2010)
  • Author(s): 近藤智
  • Organizer: Number theory seminar
  • Place of Presentation: 韓国・韓国高等研究所
  • Year and Date: 2010-03-11
• [Presentation] K-theory of elliptic curves and stabilities (2009)
  • Author(s): 安田正大
  • Organizer: 野田モジュラー多様体研究集会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2009-12-24
• [Presentation] ドリンフェルト加群のモジュライの代数的K群の計算 (2009)
  • Author(s): 近藤智
  • Organizer: 野田モジュラー多様体研究集会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2009-12-22
• [Presentation] Regulators, periods, and special values of automorphic form L-functions over function fields (2009)
  • Author(s): 安田正大
  • Organizer: t-motives : Hodge structures, transcendence and other motivic aspects
  • Place of Presentation: カナダ・バンフ国際研究センター
  • Year and Date: 2009-09-28