Eisenstein Cohomology and ratios of critical values of Rankin-Selberg L-functions

TL;DR

This paper presents new results on Eisenstein cohomology for GL(N) and establishes algebraicity of ratios of critical values of Rankin-Selberg L-functions for specific GL(n) x GL(n') cases, advancing understanding of their arithmetic properties.

Contribution

It introduces novel results on Eisenstein cohomology of GL(N) and proves algebraicity theorems for ratios of critical L-values in specific cases, extending previous work in automorphic forms.

Findings

Results on rank-one Eisenstein cohomology of GL(N) for odd N

Algebraicity theorems for ratios of critical values of Rankin-Selberg L-functions

Advancement in understanding the arithmetic nature of L-values

Abstract

This is an announcement of results on rank-one Eisenstein cohomology of GL(N), with N > 1 an odd integer, and algebraicity theorems for ratios of successive critical values of certain Rankin-Selberg L-functions for GL(n) x GL(n') when n is even and n' is odd.