Eisenstein Cohomology for GL(N) and ratios of critical values of Rankin-Selberg L-functions
arXiv:1405.6513
Abstract
The aim of this article is to study rank-one Eisenstein cohomology for the group GL(N)/F, where F is a totally real field extension of Q. This is then used to prove rationality results for ratios of successive critical values for Rankin-Selberg L-functions for GL(n) x GL(n') over F with the parity condition that nn' is even. The key idea is to interpret Langlands's constant term theorem in terms of Eisenstein cohomology.
82 pages, including Appendix 1 by Uwe Weselmann and Appendix 2 by Chandrasheel Bhagwat and A. Raghuram. Many local edits and improvements in the 2nd version