
Journal of Lie Theory 22 (2012), No. 4, 10911107 Copyright Heldermann Verlag 2012 On the Inner Product of Certain Automorphic Forms and Applications Goran Muic Dept. of Mathematics, University of Zagreb, Bijenicka cesta 30, 10000 Zagreb, Croatia gmuic@math.hr [Abstractpdf] \def\R{{\Bbb R}} Let $\Gamma\subset {\rm SL}_2(\R)$ be a discrete subgroup such that the quotient $\Gamma\backslash{\rm SL}_2(\R)$ has a finite volume. In this paper we compute the Petersson inner product of automorphic cuspidal forms with Poincar\' e series constructed out of matrix coefficients of a holomorphic discrete series of lowest weight $m\ge 3$. We apply the result to give new and representationtheoretic proofs of previous results, some of which were known to Petersson, and are anyway not surprising to experts. Keywords: Fuchsian groups, automorphic forms, modular forms, Poincare series. MSC: 11F70, 11F20 [ Fulltextpdf (317 KB)] for subscribers only. 