Non-Vanishing of Derivatives of L-Functions of Hilbert Modular Forms in The Critical Strip

2020/06/04 by Hamieh, Alia, Raji, Wissam
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2006.02997

Abstract

In this paper, we show that, on average, the derivatives of L-functions of cuspidal Hilbert modular forms with sufficiently large weight k do not vanish on the line segments \Im(s)=t₀, \Re(s)∈((k-1)/(2),(k)/(2)-ε)∪((k)/(2)+ε,(k+1)/(2)). This is analogous to the case of classical modular forms.

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