Non-vanishing of derivatives of L-functions associated to cusp forms of half-integral weight in the plus space

Abstract

We show a non-vanishing result for the derivatives of L-functions associated to cuspidal Hecke eigenforms of half-integral weight in plus space. In particular, we show that for large weights, ∑j=1d1⟨fk,j,fk,j⟩dndsn[L∗(fk,j|W4,s)]does not vanish at any point s= σ+ it with t= t, k/ 2 - 1 / 4 < σ< k/ 2 + 3 / 4. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.