On the distribution of Satake parameters for Siegel modular forms

Abstract

We prove a harmonically weighted equidistribution result for the $p$-th Satake parameters of the family of automorphic cuspidal representations of $\mathrm{PGSp}(2n)$ of fixed weight $\mathtt{k}$ and prime-to-$p$ level $N\to \infty$. The main tool is a new asymptotic Petersson formula for $\mathrm{GSp}(2n)$ in the level aspect.

Accepted by Doc. Math. 24 (2019), 677-747

References in corpus (2)

• An equidistribution theorem for holomorphic Siegel modular forms for $GS{p}_4$
• Integral representation and critical $L$-values for holomorphic forms on $GS{p}_{2n}\times G{L}_1$

Cited by in corpus (2)

• On the standard $L$-function for $GS{p}_{2n}\times G{L}_1$ and algebraicity of symmetric fourth $L$-values for $G{L}_2$
• Equidistribution theorems for holomorphic Siegel cusp forms of general degree: the level aspect