On the non-vanishing of L-functions associated to cusp forms of half-integral weight

TL;DR

This paper establishes new criteria ensuring the non-vanishing of L-functions linked to half-integral weight cusp forms, advancing understanding of their analytic properties.

Contribution

It strengthens Muić's non-vanishing criterion for Poincaré series and applies it to prove non-vanishing results for associated L-functions.

Findings

Proved a strengthened non-vanishing criterion for Poincaré series.

Established non-vanishing of L-functions for half-integral weight cusp forms.

Extended previous results to broader classes of automorphic forms.

Abstract

We prove a strengthening of Mui\'c's integral non-vanishing criterion for Poincar\'e series on unimodular locally compact Hausdorff groups and use it to prove a result on non-vanishing of L-functions associated to cusp forms of half-integral weight.