Study of Fourier-Jacobi expansions for Siegel modular forms of degree two and associated special functions

• Project/Area Number: 18740010
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Ehime University (2006, 2008); Seikei University (2007)
• Principal Investigator: HIRANO Miki Ehime University, 理工学研究科, 教授 (80314946)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,730,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000); Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
• Keywords: フーリエ・ヤコビ型球関 / フーリエ・ヤコビ展開 / 保型L-関数 / ジーゲル保型形式 / ホイッタカー関数 / フーリエ・ヤコビ型球関教 / 保型L-関教 / フーリエ・ヤコビ型球関数

Research Abstract

本研究課題の主たる研究対象であるフーリエ・ヤコビ型球関数の決定についての予備研究において、十分に満足いく成果をあげることができた。主な成果は、Sp(3,R)のある一般主系列表現に対するホイッタカー関数およびGL(3,C)のクラス1でない主系列表現に対するホイッタカー関数の明示公式である。これらは保型形式に関連した球関数として最重要なものの一つであり、保型形式論とりわけ保型L-関数への応用が期待される。

Research Products

• [Journal Article] Calculus of principal series Whittaker functions on GL(3,C) (2009)
  • Author(s): M. Hirano, T. Oda
  • Journal Title: Journal of Functional Analysis 256 Pages: 2222-2267
  • Peer Reviewed
• [Journal Article] Calaulus of prinaipal series Whittaker funcfions on GL(3,C) (2009)
  • Author(s): Miki Hirano, Takayuki Oda
  • Journal Title: Jaul-Nal of Functionaf Aualysis 256 Pages: 2222-2267
  • Peer Reviewed
• [Journal Article] Whittaker functions for PJ-principal series representations of Sp(3,R) (2007)
  • Author(s): M. Hirano, T. Ishii, T. Oda
  • Journal Title: Advances in Mathematics 215 Pages: 734-765
  • Peer Reviewed
• [Journal Article] Propagation formula for principal series Whittaker functions on GL(3,C) (2007)
  • Author(s): M. Hirano
  • Journal Title: 成蹊大学理工学研究報告 44 Pages: 17-23
  • NAID: 110007612222
• [Journal Article] Whiftaka funetions for P_J-principal sevies representations of Sp (3.R) (2007)
  • Author(s): Miki, Hirano・Taku, Jshii・Takayuki, Oka
  • Journal Title: Adcances in mathematics 215 Pages: 734-765
  • Peer Reviewed
• [Journal Article] Propagation Formula for principal sevies Whitaken functions on GL(3.C) (2007)
  • Author(s): Miki, Hirano
  • Journal Title: 成蹊大学 理工学研究報告 44-2 Pages: 17-23
• [Journal Article] Confluence from Siegel-Whittaker functions to Whittaker functions on Sp(2,R) (2006)
  • Author(s): M. Hirano, T. Ishii, T. Oda
  • Journal Title: Mathematical Proceedings of the Cambridge Philosophical Society 141 Pages: 15-31
  • Peer Reviewed
• [Journal Article] Conflueuce from Siegel-Whittaker functions to Whittaker functions on Sp(2.1R) (2006)
  • Author(s): Miki Hirano, Taku Ishii, Takayuki Oda
  • Journal Title: Mathematical Proceedings of the Canbroidge Philosophical Society 141-1 Pages: 15-31
• [Journal Article] Whiffaker functions for Pj-priucipal series representations of Sp(3.1R)
  • Author(s): Miki Hirano, Taku Ishii, Takayuki Oda
  • Journal Title: Adrances in Mathowatics (to appear)