Can I read Eisenstein cohomology for orthogonal groups and the special values of $L$-functions for ${\rm GL}_1 \times {\rm O}(2n)$ on EtoBox?

Eisenstein cohomology for orthogonal groups and the special values of $L$-functions for ${\rm GL}_1 \times {\rm O}(2n)$ by Bhagwat, Chandrasheel; Raghuram, A. is a scholarly article available to read on EtoBox.

What is Eisenstein cohomology for orthogonal groups and the special values of $L$-functions for ${\rm GL}_1 \times {\rm O}(2n)$ about?

For an even positive integer $n$, we study rank-one Eisenstein cohomology of the split orthogonal group ${\rm O}(2n+2)$ over a totally real number field $F.$ This is used to prove a rationality result for the ratios of successive critical values of degree-$2n$ Langlands $L$-functions associated to the group ${\rm GL}_1 \times {\rm O}(2n)$ over $F$. The case $n=2$ specializes to classical results of Shimura on the special values of Rankin - Selberg $L$-functions attached to a pair of Hilbert modular forms.

Author

Bhagwat, Chandrasheel; Raghuram, A.

Published

2020

Language

EN