Let \( \Gamma \) be a congruence subgroup of \( Sp_{2n}(\mathbb Z)\). Using Poincaré series of \( K\)-finite matrix coefficients of integrable discrete series representations of \( Sp_{2n}(\mathbb R)\), we construct a spanning set for the space \( S_m(\Gamma)\) of Siegel cusp forms of weight \( m\in \mathbb Z_{>2n}\). We study the non-vanishing of certain elements of this spanning set and compute the Petersson inner product of corresponding cuspidal automorphic forms, thereby recovering a representation-theoretic proof of some well-known results on the reproducing kernel function of \( S_m(\Gamma)\).
On a family of Siegel Poincaré series
17.10.2023 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: