The Critical Numbers of Rankin-Selberg Convolutions of Cohomological Representations

TL;DR

This paper investigates the critical points of Rankin-Selberg convolutions for cohomological automorphic representations, linking these points to specific subrepresentations of associated finite-dimensional representations.

Contribution

It provides a parametrization of critical numbers of Rankin-Selberg convolutions in terms of subrepresentations, extending understanding of automorphic L-functions.

Findings

Parametrization of critical numbers via subrepresentations

Connection between automorphic representations and finite-dimensional representations

Enhanced understanding of Rankin-Selberg convolution critical points

Abstract

We study the critical numbers of the Rankin-Selberg convolution of arbitrary pairs of cohomological cuspidal automorphic representations and we parametrize these critical numbers by certain 1-dimensional subrepresentations attached to the corresponding pair of finite-dimensional representations of the related general linear groups.