Uniform Integrality of critical values of the Rankin-Selberg L-function for \rm GL_n× \rm GL_n-1

2023/08/23 by Takashi Hara, Hara, Takashi, Tadashi Miyazaki +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2308.12200

openalex publication_date 2023/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

After introducing the notion of uniform integrality of critical values of the Rankin-Selberg L-functions for GL_n× GL_n-1, we study it when the base field is totally imaginary. For this purpose, we adopt specific models of highest weight representations of the general linear groups, construct the Eichler-Shimura classes for GL_n and GL_n-1 in an explicit manner, and then evaluate the cohomological cup product of them, by making the best use of Gel'fand-Tsetlin basis.

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