A spectral identity for second moments of Eisenstein series of O(n, 1)

Abstract

Let H=O(n)xO(1) be an anisotropic subgroup of G=O(n, 1) and let A be the adele ring of k=Q. Consider the periods of an Eisenstein series on G against a form F on H. Relying on a variant of Levi-Sobolev spaces, we describe certain Poincar\'e series as fundamental solutions for the laplacian, and use them to establish a spectral identity concerning the second moments (in F-aspect) of the Eisenstein series.