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.