L-functions and periods of automorphic forms

Abstract: This is a report on recent work with Grobner and Lin on the critical values of Rankin-Selberg L-functions of GL(n)xGL(n-1) over CM fields. By reinterpreting these critical values in terms of automorphic periods of holomorphic automorphic forms on unitary groups, we show that the automorphic periods of holomorphic forms can be factored as products of coherent cohomological forms, compatibly with a motivic factorization predicted by the Tate conjecture. All of these results are conditional on a conjecture on non-vanishing of twists of automorphic L-functions of GL(n) by anticyclotomic characters of finite order, and are stated under a certain regularity condition.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar