Original scientific paper
https://doi.org/10.64785/mc.30.2.1
Orthogonality relations for Poincaré series
Sonja Žunar
orcid.org/0000-0002-4747-7805
; Faculty of Geodesy, University of Zagreb, Zagreb, Croatia
*
* Corresponding author.
Abstract
Let 𝐺 be a connected semisimple Lie group with finite center. We prove a formula for the inner product of
two cuspidal automorphic forms on 𝐺 that are given by Poincaré series of 𝐾-finite matrix coefficients of an integrable
discrete series representation of 𝐺. As an application, we give a new proof of a well-known result on the Petersson
inner product of certain vector-valued Siegel cusp forms. In this way, we extend results previously obtained by Muić for
cusp forms on the upper half-plane, i.e., in the case when \{ G=SL_{2}(\mathbb{R})\}.
Keywords
Poincaré series; Petersson inner product; orthogonality relations; automorphic forms; Siegel cusp forms
Hrčak ID:
335656
URI
Publication date:
22.9.2025.
Visits: 446 *