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 $G^{\prime }\subset G$. As a consequence we obtain an explicit $G^{\prime }(\mathbb{A})$-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.

Convergence criterion improved. Small changes in presentation. 39 pages, 10 figures