Special Values of L-functions for Orthogonal Groups

TL;DR

This paper announces rationality results for critical L-values associated with GL(1) and SO(n, n) over rationals, using Eisenstein cohomology for orthogonal groups, advancing understanding of special L-function values.

Contribution

It introduces new rationality results for critical L-values of degree-2n L-functions for orthogonal groups, based on Eisenstein cohomology techniques.

Findings

Rationality results for critical L-values established.

Connections between Eisenstein cohomology and L-values demonstrated.

Framework applicable to orthogonal groups over rationals.

Abstract

This is an announcement of certain rationality results for the critical values of the degree-2n L-functions attached to GL(1) $\times$ SO(n, n) over $\mathbb Q$ for an even positive integer n. The proof follows from studying the rank-one Eisenstein cohomology for SO(n + 1, n + 1).