Resolvent type trace formulas, automorphic forms and number theory

• Project/Area Number: 19540039
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyushu University
• Principal Investigator: GON Yasuro Kyushu University, 大学院・数理学研究院, 准教授 (30302508)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 数論 / 保型形式 / ディリクレ級数 / 跡公式 / 総双曲 / 対相関 / レギュレーター / 総実代数体 / ヒルベルトモジュラー群 / ヒルベルトモジュラー多様体 / セルバーグ跡公式 / セルバーグ型ゼータ関数 / 実二次体 / 双曲多様体 / 重み付軌道積分 / セルバーグぜータ関数 / ルエルゼータ関数

Research Abstract

Automorphic forms are important functions that appear when researching number theory. The trace formula is one of the most important tools in studying automorphic forms. We proved various formulas on some types of trace formulas, which is useful for application to number theory. Based on our results, we also proved analytic properties of Ruelle zeta functions and Selberg zeta functions.

Research Products

• [Journal Article] Differences of the Selberg trace formula and Selberg type zeta functions for Hilbert modular surfaces (2010)
  • Author(s): Y.Gon
  • Journal Title: 数理解析研究所講究録 1715 Pages: 64-74
• [Journal Article] The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps (2010)
  • Author(s): Y.Gon, J.Park
  • Journal Title: Math.Ann. 346 Pages: 719-767
  • Peer Reviewed
• [Journal Article] Differences of the Selberg trace formula and Selberg type zeta functions for Hilbert modular surfaces (2010)
  • Author(s): Y.Gon
  • Journal Title: 数理解析研究所講究録 Volume: 1715 Pages: 64-74
• [Journal Article] The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps (2010)
  • Author(s): Y. Gon, J. Park
  • Journal Title: Math.Ann. 346 Pages: 719-767
  • Peer Reviewed
• [Journal Article] Ruelle zeta function for odd dimensional hyperbolic manifolds with cusps (2008)
  • Author(s): Y.Gon, J.Park
  • Journal Title: Proc. Japan Acad. 84A Pages: 1-4
  • NAID: 40015807924
  • Peer Reviewed
• [Journal Article] Ruelle zeta function for odd dimensional hyperbolic manifolds with cusps (2008)
  • Author(s): Y. Gon, J. Park
  • Journal Title: Proc.Japan Acad. 84A Pages: 1-4
  • NAID: 40015807924
  • Peer Reviewed
• [Journal Article] Ruelle zeta function for odd dimensional hyperbolic manifolds with cusps (2008)
  • Author(s): Y.Gon, J. Park
  • Journal Title: Proc. Japan Acad. Ser. A Math. Sci. 84 Pages: 1-4
  • NAID: 40015807924
  • Peer Reviewed
• [Journal Article] Multiple q-Mahler measures and zeta functions (2007)
  • Author(s): Y.Gon, N.Kurokawa, H.Oyanagi
  • Journal Title: J.Number Theory 124 no.2 Pages: 328-345
  • Peer Reviewed
• [Journal Article] Multiple q-Mahler measures and zeta functions (2007)
  • Author(s): Y. Gon, N. Kurokawa, H. Oyanagi
  • Journal Title: J.Number Theory 124 no.2 Pages: 328-345
  • Peer Reviewed
• [Journal Article] Multiple q-Mahler measures and zeta functions (2007)
  • Author(s): Y.Gon, N. Kurokawa and H. Oyanagi
  • Journal Title: J. Number theory 124 Pages: 328-345
  • Peer Reviewed
• [Presentation] Mahler measures and their generalization (2011)
  • Author(s): 権寧魯
  • Organizer: The Eve of IMI and FM, Ito One Day Workshop
  • Place of Presentation: 九州大学
  • Year and Date: 2011-03-29
• [Presentation] Truncated Selberg type Dirichlet series and asymptotic formulas (2010)
  • Author(s): 権寧魯
  • Organizer: 研究集会"Zetas and Limit Laws 2010"
  • Place of Presentation: 沖縄コンベンションセンター
  • Year and Date: 2010-11-07
• [Presentation] Selberg type zeta functions for the Hilbert modular group of a real quadratic field (2010)
  • Author(s): 権寧魯
  • Organizer: 仙台整数論集会
  • Place of Presentation: 東北大学
  • Year and Date: 2010-10-09
• [Presentation] Selberg type zeta functions for the Hilbert modular group of a real quadratic field (2010)
  • Author(s): Y.Gon
  • Organizer: 仙台整数論研究集会
  • Place of Presentation: 東北大学(宮城県)
  • Year and Date: 2010-10-09
• [Presentation] Selberg跡公式,Selbergゼータ関数 (2010)
  • Author(s): 権寧魯
  • Organizer: 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"
  • Place of Presentation: 山中温泉河鹿荘ロイヤルホテル
  • Year and Date: 2010-09-06
• [Presentation] ヒルベルトモジュラー曲面に対するセルバーグ跡公式の差分とセルバーグ型ゼータ関数 (2010)
  • Author(s): 権寧魯
  • Organizer: RIMS研究集会「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: 東京大学
  • Year and Date: 2010-01-19
• [Presentation] ヒルベルトモジュラー曲面に対するセルバーグ跡公式の差分とセルバーグ型ゼータ関数 (2010)
  • Author(s): 権寧魯
  • Organizer: RIMS研究集会「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: 東京大学
  • Year and Date: 2010-01-19
• [Presentation] Selberg type zeta functions for the Hilbert modular varieties (2009)
  • Author(s): 権寧魯
  • Organizer: 研究集会"Zetas and Limit Laws 2009"
  • Place of Presentation: カルチャーリゾートフェストーネ
  • Year and Date: 2009-11-16
• [Presentation] Selberg zeta関数の行列式表示 (2008)
  • Author(s): 権寧魯
  • Organizer: 研究集会"ゼータ関数の行列式表示"
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-03-27
• [Presentation] オイラー五角数定理から保型形式へ,ENCOUNTER with MATHEMATICS (2007)
  • Author(s): 権寧魯
  • Organizer: 第42回Euler生誕300年
  • Place of Presentation: 中央大学
  • Year and Date: 2007-12-01
• [Presentation] Generalized Mahler measures and multiple q-Mahler measures (2007)
  • Author(s): 権寧魯
  • Organizer: Postech-Japan Number Theory Symposium
  • Place of Presentation: Postech, Korea
  • Year and Date: 2007-04-28