Periods of automorphic forms over reductive subgroups

Abstract

We present a regularization procedure of period integrals of automorphic forms on a group G over an arbitrary reductive subgroup G ′ ⊂ G.As a consequence we obtain an explicit G ′ (A)-invariant functional on the space of automorphic forms on G whose exponents avoid certain prescribed hyperplanes.We also provide a necessary and sufficient condition for convergence of period integrals of automorphic forms in terms of their exponents.

Topics & Concepts