On the non-vanishing of Poincaré series on irreducible bounded symmetric domains

2025/01/12 by Žunar, Sonja
#11F55 #11F70 #22E46 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2501.06876

Abstract

Let \mathcal D≡ G/K be an irreducible bounded symmetric domain. Using a vector-valued version of Muić's integral non-vanishing criterion for Poincaré series on locally compact Hausdorff groups, we study the non-vanishing of holomorphic automorphic forms on \mathcal D that are given by Poincaré series of polynomial type and correspond via the classical lift to the Poincaré series of certain K -finite matrix coefficients of integrable discrete series representations of G . We provide an example application of our results in the case when G=SU(p,q) and K=\mathrm S(\mathrm U(p)×\mathrm U(q)) with p≥ q≥1 .

Related

• Construction and non-vanishing of a family of vector-valued Siegel Poincaré series
• On vector-valued automorphic forms on bounded symmetric domains
• Non-vanishing of vector-valued Poincaré series
• On a family of Siegel Poincaré series
• On the Non-Vanishing of Poincaré Series on the Metaplectic Group