A duality relation for certain triple products of automorphic forms
type: Item
instance of: scholarly article
title: A duality relation for certain triple products of automorphic forms
zbMATH Open document ID: 1345.11027
author: András Biró
published in: Israel Journal of Mathematics
publication date: 2013-02-07T00:00:00Z
review text: In this paper, a Poisson-type summation formula for weight \(2k+1/2\) (\(k \in \mathbb N_0\)) is proved. The weights in the formula can be expressed as triple products of theta products and Maaß forms. The analogue of the Fourier transform in the summation formula is played by the Wilson transform of type II which was introduced by \textit{W. Groenevelt} [Int. Math. Res. Not. 2003, No. 52, 2779--2817 (2003; Zbl 1079.33005)]. The methods of the proof involve spectral theory and make frequent use of geodesic polar coordinates.
reviewed by: Nikolaos Diamantis
Mathematics Subject Classification ID: 11F12
Mathematics Subject Classification ID: 11F72
zbMATH DE Number: 6135111
zbMATH Keywords: Poisson summation formula
zbMATH Keywords: Maass cusp forms
zbMATH Keywords: spectral decomposition
zbMATH Keywords: Wilson function transform
MaRDI profile type: Publication
full work available at URL: s11856-012-0041-0
OpenAlex ID: W2059349451
cites work: A relation between triple products of weight 0 and weight 1/2 cusp forms
cites work: A new approach to the spectral theory of the fourth moment of the Riemann zeta-function
cites work: Hyperbolic distribution problems and half-integral weight Maass forms
cites work: Fourier coefficients of the resolvent for a Fuchsian group.
cites work: Q5693275
cites work: Wilson function transforms related to Racah coefficients
cites work: Q4515165
cites work: Q4846158
cites work: The twelfth moment of central values of Hecke series
cites work: Q4012861
cites work: Heegner points, cycles and Maass forms
cites work: Q4831670
cites work: Rankin-Selberg without unfolding and bounds for spherical Fourier coefficients of Maass forms
DOI: 10.1007/S11856-012-0041-0
description: scientific article; zbMATH DE number 6135111