Eisenstein Cohomology for GL(N) and ratios of critical values of Rankin-Selberg L-functions

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.

arXiv comment82 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

References in corpus (1)

• On Deligne's periods for tensor product motives

Cited by in corpus (7)

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• Harish-Chandra Modules over $\mathbb{Z}$
• Endoscopy and the cohomology of GL(n)
• Galois representations associated with a non-selfdual automorphic representation of GL(3)
• Class group twists and Galois averages of ${\mathrm{GL}}_n$-automorphic $L$-functions
• Special Values of L-functions for Orthogonal Groups