Ratios of periods for tensor product motives

TL;DR

This paper establishes period relations for tensor product motives, providing a motivic interpretation for algebraicity results related to critical values of Rankin-Selberg L-functions for GL(n)×GL(n').

Contribution

It proves new period relations for Deligne's periods of tensor product motives, linking them to algebraicity of critical L-value ratios.

Findings

Period relations for Deligne's periods are established.

Motivic interpretation for algebraicity of L-value ratios is provided.

Connections to Rankin-Selberg L-functions are clarified.

Abstract

In this article we prove some period relations for the ratio of Deligne's periods for certain tensor product motives. These period relations give a motivic interpretation for certain algebraicity results for ratios of successive critical values for Rankin-Selberg L-functions for ${\rm GL}_n \times {\rm GL}_{n'}$ proved by G\"unter Harder and the second author.