A duality relation for certain triple products of automorphic forms
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.
scientific article; zbMATH DE number 6135111