Corpus ID: 19681852

# On the distribution of Satake parameters for Siegel modular forms

@article{Knightly2016OnTD,
title={On the distribution of Satake parameters for Siegel modular forms},
author={Andrew H. Knightly and Charles Li},
journal={arXiv: Number Theory},
year={2016}
}
• Published 2016
• Mathematics
• arXiv: Number Theory
We prove a harmonically weighted equidistribution result for the $p$-th Satake parameters of the family of automorphic cuspidal representations of $\operatorname{PGSp}(2n)$ of fixed weight $\mathtt{k}$ and prime-to-$p$ level $N\to \infty$. The main tool is a new asymptotic Petersson formula for $\operatorname{GSp}(2n)$ in the level aspect.
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We prove an explicit integral representation -- involving the pullback of a suitable Siegel Eisenstein series -- for the twisted standard $L$-function associated to a holomorphic vector-valued SiegelExpand