Speaker
Sonja Zunar
(University of Zagreb)
Description
Let $ \Gamma $ be a congruence subgroup of $ \mathrm{Sp}_{2n}(\mathbb Z) $. Using Poincaré series of $ K $-finite matrix coefficients of integrable discrete series representations of $ \mathrm{Sp}_{2n}(\mathbb R) $, we construct a spanning set for the space $ S_\rho(\Gamma) $ of Siegel cusp forms for $ \Gamma $ of weight $ \rho $, where $ \rho $ is an irreducible polynomial representation of $ \mathrm{GL}_n(\mathbb C) $ of highest weight $ \omega=(\omega_1,\ldots,\omega_n)\in\mathbb Z^n $ with $ \omega_1\geq\ldots\geq\omega_n>2n $. We study the non-vanishing of constructed Siegel cusp forms and their role in the theory of Siegel modular forms.
Primary author
Sonja Zunar
(University of Zagreb)
