Moments of Spinor L-Functions and symplectic Kloosterman sums

TL;DR

This paper calculates the second moment of spinor L-functions at central points for Siegel modular forms on large prime level congruence subgroups, providing insights into their non-vanishing properties.

Contribution

It introduces a new computation of the second moment of spinor L-functions for Siegel modular forms at high levels, with applications to non-vanishing results.

Findings

Computed the second moment of spinor L-functions at central points.

Established non-vanishing results for these L-functions.

Analyzed behavior on congruence subgroups of large prime level.

Abstract

We compute the second moment of spinor $L$-functions at central points of Siegel modular forms on congruence subgroups of large prime level $N$ and give applications to non-vanishing.