Non-vanishing of derivatives of L-functions of Hilbert modular forms in the critical strip

Abstract

In this paper, we show that, on average, the derivatives of L-functions of cuspidal Hilbert modular forms with sufficiently large parallel weight k do not vanish on the line segments I(s) = t, R(s)∈(k-12,k2-ϵ)∪(k2+ϵ,k+12). This is analogous to the case of classical modular forms. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.