Non-vanishing of -functions of Hilbert modular forms inside the critical strip
Tom 185 / 2018
Acta Arithmetica 185 (2018), 333-346
MSC: Primary 11F41, 11F67; Secondary 11F30, 11F11, 11F12, 11N75.
DOI: 10.4064/aa170721-10-7
Opublikowany online: 14 September 2018
Streszczenie
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.
