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NCTS Number Theory Seminar
10:00 - 11:00, August 5, 2022 (Friday)
Cisco Webex, Online seminar
(線上演講 Cisco Webex)
An Integrality of Critical Values of Rankin-Selberg L-functions for GL(n+1)×GL(n)
Kenichi Namikawa (Tokyo Denki University)


The study of period integrals is one of fundamental objects for the study of special values of L-functions. In this talk, we consider a refinement of the generalized modular symbol method due to Kazhdan-Mazur-Schmidt, and we study period integrals for Rankin-Selberg L-functions for GL(n+1)×GL(n) if the base fields are totally imaginary. Namely, by using an integral model of local systems on symmetric spaces for GL(n) and an explicit formula for the archimedean local zeta integrals, we prove an algebraicity of critical values of Rankin-Selberg L-functions for GL(n+1)×GL(n) with respect to an appropriate period. Furthermore, we also propose a formulation for integral properties of these critical values. This is a joint work with Takashi Hara (Tsuda University) and Tadashi Miyazaki (Kitasato University).

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