Non-vanishing of $L$-functions of Hilbert modular forms inside the critical strip
Volume 185 / 2018
Acta Arithmetica 185 (2018), 333-346
MSC: Primary 11F41, 11F67; Secondary 11F30, 11F11, 11F12, 11N75.
DOI: 10.4064/aa170721-10-7
Published online: 14 September 2018
Abstract
We show that, on average, the $L$-functions of cuspidal Hilbert modular forms with sufficiently large weight $k$ do not vanish on the line segments $\Im (s)=t_{0}$, $\Re (s)\in ((k-1)/2,k/2-\epsilon )\cup (k/2+\epsilon ,(k+1)/2)$. This is analogous to the case of classical modular forms.
