On the Distribution of Satake Parameters for Siegel Modular Forms

  • Andrew Knightly

    Department of Mathematics and Statistics, University of Maine, Orono, ME 04469-5752, USA
  • Charles Li

    Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
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Abstract

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

Cite this article

Andrew Knightly, Charles Li, On the Distribution of Satake Parameters for Siegel Modular Forms. Doc. Math. 24 (2019), pp. 677–747

DOI 10.4171/DM/692