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 weight $k$ do not vanish on the line segments $\Im (s)=t_0$, $\Re (s)\in (\frac{k-1}{2},\frac{k}{2}-\epsilon )\cup (\frac{k}{2}+\epsilon ,\frac{k+1}{2})$. This is analogous to the case of classical modular forms.