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

Research Project

Project/Area Number	24540022
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
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)	2012-04-01 – 2015-03-31
Project Status	Completed (Fiscal Year 2014)
Budget Amount *help	¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000) Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000) Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000) Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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 / ランキン・セルバーグ型ゼータ積分
Outline of Final Research Achievements	We reaped a satisfactory result in a preliminary and a similar study to the main theme. The principal results are explicit evaluations of the zeta integrals of GL(3,C)×GL(2,C) which is an application of our explicit formulas of the non-class 1 principal series Whittaker functions on GL(3,C). These are important for the explicit theory of automorphic forms and their L-functions.

Report

(4 results)