Period relations for Rankin-Selberg convolutions for $\mathrm{GL}(n)\times\mathrm{GL}(n)$

TL;DR

This paper investigates the rationality and period relations of critical values of Rankin-Selberg L-functions for GL(n)×GL(n) over number fields with CM, extending previous work with a modular symbol approach.

Contribution

It establishes new period relations and rationality results for critical L-values of GL(n)×GL(n) using modular symbols over general number fields.

Findings

Proves rationality of certain critical L-values.

Establishes period relations for Rankin-Selberg convolutions.

Extends results to number fields containing CM fields.

Abstract

In this paper, we study the special values of Rankin-Selberg L-functions as a continuation of [LLS24]. Utilizing the modular symbol approach, we prove the rationality and period relations for some critical values of Rankin-Selberg L-functions for $\mathrm{GL}(n)\times\mathrm{GL}(n)$ over any number field that contains a CM field.