  We present a pairing of automorphic distributions that applies in situations
where a Lie group acts with an open orbit on a product of generalized flag
varieties. The pairing gives meaning to an integral of products of automorphic
distributions on these varieties. This generalizes classical integral
representations or "Rankin-Selberg integrals" of L-functions, and gives new
constructions and analytic continuations of automorphic L-functions.
  Keywords: Automorphic forms, invariant pairings, automorphic distributions,
L-functions, analytic continuation, rapid decay.
