# 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} }

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.

#### 10 Citations

Integral representation and critical $L$-values for holomorphic forms on $GSp_{2n} \times GL_1$

- Mathematics
- 2017

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 Siegel… Expand

Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level

- Mathematics
- 2015

We formulate an explicit refinement of B\"ocherer's conjecture for Siegel modular forms of degree 2 and squarefree level, relating weighted averages of Fourier coefficients with special values of… Expand

Equidistribution theorems for holomorphic Siegel cusp forms of general degree: the level aspect

- Mathematics
- 2021

This paper is an extension of [26] and we prove equidistribution theorems for families of holomorphic Siegel cusp forms of general degree in the level aspect. Our main contribution is to estimate… Expand

On the standard L-function for
$$\mathrm{GSp}_{2n} \times \mathrm{GL}_1$$
GSp
2
n

- Mathematics
- 2020

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 Siegel cusp… Expand

On the standard L-function for GSp2n × GL1 and algebraicity of symmetric fourth L-values for GL2

- 2020

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 vectorvalued Siegel cusp… Expand

On the standard L-function for $$\mathrm{GSp}_{2n} \times \mathrm{GL}_1$$ and algebraicity of symmetric fourth L-values for $$\mathrm{GL}_2$$

- Mathematics
- Annales mathématiques du Québec
- 2020

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 Siegel cusp… Expand

N T ] 2 2 M ar 2 01 8 Integral representation and critical L-values for holomorphic forms on GSp 2 n × GL 1

- 2018

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 vectorvalued Siegel cusp… Expand

The Relative Trace Formula in Analytic Number Theory

- Mathematics
- 2019

We discuss a variety of applications of the relative trace formula of Kuznetsov type in analytic number theory and the theory of automorphic forms.

N T ] 2 2 M ar 2 01 8 On the standard L-function for GSp 2 n × GL 1 and algebraicity of symmetric fourth L-values for GL 2

- 2018

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 vectorvalued Siegel cusp… Expand

Correction to: On Fourier coefficients of Siegel modular forms of degree two with respect to congruence subgroups

- Mathematics
- Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
- 2019

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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 Siegel… Expand