Resolvent type trace formulas, automorphic forms and zeta functions

• Project/Area Number: 26400017
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyushu University
• Principal Investigator: GON Yasuro 九州大学, 数理学研究院, 准教授 (30302508)
• Co-Investigator(Renkei-kenkyūsha): TSUZUKI Masao 上智大学, 理工学部, 教授 (80296946)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 数論 / 保型形式 / 跡公式 / セルバーグ型ゼータ関数 / ヒルベルトモジュラー曲面 / 正規化行列式 / スペクトルゼータ関数 / スペクトルテータ関数 / 離散系列表現 / Siegel-Whittaker関数 / 合流型超幾何関数 / 部分的変形 / 保型形式の周期 / セルバーグ跡公式 / 純三次体

Outline of Final Research Achievements

We studied resolvent type trace formulas, automorphic forms and zeta functions.　Based on our results, we proved analytic properties of certain Dirichlet series　constructed from periods of automorphic forms. We also determined the location of　poles and residues. Besides, we obtained an simple and explicit integral representation of Siegel-Whittaker functions on Sp(2,R) for the large discrete series representations.

Research Products

• [Int'l Joint Research] University of Tuebingen(Germany)
• [Journal Article] An explicit integral representation of Siegel-Whittaker functions on Sp(2,R) for the large discrete series representations (2017)
  • Author(s): Yasuro Gon and Takayuki Oda
  • Journal Title: Contemporary Mathematics Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Dirichlet series constructed from periods of automorphic forms (2015)
  • Author(s): Yasuro Gon
  • Journal Title: Mathematische Zeitschrift Volume: 281 Issue: 3-4 Pages: 747-773
  • DOI: 10.1007/s00209-015-1506-8
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Differences of the Selberg trace formula and Selberg type zeta functions for Hilbert modular surfaces (2015)
  • Author(s): Yasuro Gon
  • Journal Title: Journal of Number Theory Volume: 147 Pages: 396-453
  • DOI: 10.1016/j.jnt.2014.07.019
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Selberg zeta functions for Hilbert modular groups and determinants of restricted Laplacians (2016)
  • Author(s): Yasuro Gon
  • Organizer: Oberseminar Analysis und Zahlentheorie
  • Place of Presentation: University of Tuebingen
  • Year and Date: 2016-08-30
• [Presentation] An explicit integral representation of Siegel-Whittaker functions on Sp(2,R) for the large discrete series representations (2016)
  • Author(s): Yasuro Gon
  • Organizer: International conference "Geometry, Representation Theory, and Differential Equations"
  • Place of Presentation: 九州大学
  • Year and Date: 2016-02-18
  • Int'l Joint Research / Invited
• [Presentation] Selberg type zeta functions for PSL(2) over rings of pure cubic integers (2014)
  • Author(s): Yasuro Gon
  • Organizer: Zeta functions in OKINAWA 2014
  • Place of Presentation: 沖縄コンベンションセンター
  • Year and Date: 2014-10-25