Spectral summation formula for GSp(4) and moments of spinor L-functions

TL;DR

This paper computes the first and second moments of the spinor L-function at the central point for Siegel modular forms of large weight, providing insights into their non-vanishing properties with improved error estimates.

Contribution

It introduces a spectral summation formula for GSp(4) that enables precise moment calculations of spinor L-functions, advancing understanding of their behavior.

Findings

Calculated the first and second moments with power saving error terms.

Established non-vanishing results for spinor L-functions.

Enhanced the spectral summation techniques for GSp(4).

Abstract

We compute the first and second moment of the spinor L-function at the central point of Siegel modular forms of large weight k with power saving error term and give applications to non-vanishing.