spherical functions on real reductive groups and archimedean zeta integrals

2015 Fiscal Year Final Research Report

• Project/Area Number: 24740025
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Seikei University
• Principal Investigator: Ishii Taku 成蹊大学, 理工学部, 准教授 (60406650)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 保型形式 / 保型L関数 / Whittaker関数 / アルキメデスゼータ積分

Outline of Final Research Achievements

The aim of our study is to establish analytic properties of automorphic L-functions via the integral representations method. We compute the archimedean zeta integrals which are the integral transforms of generalized spherical functions on real reductive Lie groups. As a consequence we prove the entireness, the location of possible poles and functional equations for some automorphic L-functions on GL(n) and GSp(2). Especially we show the coincidence of archimedean zeta integrals and the expected L-factors (product of Gamma functions) for the exterior square L-functions on GL(n) and the standard L-functions on GL(3)×GL(2).

Free Research Field

整数論