Study of Fourier-Jacobi type spherical functions for Siegel modular forms of degree two and its application

2011 Fiscal Year Final Research Report

• Project/Area Number: 21740020
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Ehime University
• Principal Investigator: HIRANO Miki 愛媛大学, 理工学研究科, 教授 (80314946)
• Project Period (FY): 2009 – 2011
• Keywords: フーリエ・ヤコビ型球関数 / 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

Research Abstract

We reaped a satisfactory result in a preliminary and a similar study to the main theme. The principal results are a new explicit formula of the non-calss 1 principal series Whittaker functions on GL(3, C) and its application to the associated zeta integrals. These are important for the explicit theory of automorphic forms and their L-functions.

Research Products

• [Journal Article] The Archimedean Whittaker functions on GL(3), in" Geometry and analysis of automorphic forms of several variables" (2011)
  • Author(s): Miki Hirano, Taku Ishii, Tadashi Miyazaki
  • Journal Title: World scientific Pages: 77-109
  • Peer Reviewed
• [Presentation] Archimedean Whittaker functions on GL(3), The International Symposium" Geometry and analysis of automorphic forms of several variables" (2009)
  • Author(s): Taku Ishii, Miki Hirano, Tadashi Miyazaki
  • Organizer: 東京大学大学院数理科学研究科
  • Year and Date: 2009-09-17