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Non-vanishing of $L$-functions of Hilbert modular forms inside the critical strip

Volume 185 / 2018

Alia Hamieh, Wissam Raji 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.

Authors

  • Alia HamiehDepartment of Mathematics and Statistics
    University of Northern British Columbia
    Prince George, BC V2N4Z9, Canada
    e-mail
  • Wissam RajiDepartment of Mathematics
    American University of Beirut
    P.O. Box 11-0236
    Riad El Solh
    Beirut 1107 2020, Lebanon
    e-mail

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