Moments and joint nonvanishing of symplectic $L$-functions

TL;DR

This paper derives an asymptotic formula for moments of symplectic L-functions associated with Siegel cusp forms, leading to results on non-vanishing and moment bounds.

Contribution

It provides the first asymptotic formula for these moments, enabling new non-vanishing and lower bound results for symplectic L-functions.

Findings

Asymptotic formula for moments of symplectic L-functions

Results on simultaneous non-vanishing of L-functions

Lower bounds for second moments of L-functions

Abstract

We compute an asymptotic formula for a moment involving the spinor and the standard $L$-functions for holomorphic Siegel cusp forms of degree two and large weight $k$. Applications include simultaneous non-vanishing statements and lower bounds for second moments.