On the distribution of Satake parameters for Siegel modular forms

2016/05/12 by Knightly, Andrew, Li, Charles
#11F46 #11F72 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1605.03792

Abstract

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

Related

• Weighted equidistribution theorem for Siegel modular forms of degree 2
• Computing the Satake p-parameters of Siegel modular forms
• An asymptotic formula of spectral average of central L-values on \bf GSp(2) for square free levels
• A weighted vertical Sato-Tate law for Maaß forms on \rmGSp₄
• On Exceptional Maass Forms