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 $\mathfrak {I}(s)=t_{0}$, $\mathfrak {R}(s)\in (\frac{k-1}{2},\frac{k}{2}-\epsilon )\cup (\frac{k}{2}+\epsilon ,\frac{k+1}{2})$. This is analogous to the case of classical modular forms.