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Non-vanishing of derivatives of L-functions of Hilbert modular forms in the critical strip


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.

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The authors are grateful to the referee for a number of suggestions that improved the exposition of this manuscript.

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Correspondence to Wissam Raji.

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Research of the first author is partially supported by an NSERC Discovery Grant.

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Hamieh, A., Raji, W. Non-vanishing of derivatives of L-functions of Hilbert modular forms in the critical strip. Res. number theory 7, 20 (2021).

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  • Hilbert modular forms
  • Derivatives of L-functions
  • Non-vanishing of L-functions

Mathematics Subject Classification

  • Primary 11F41
  • 11F67
  • Secondary 11F30
  • 11F11
  • 11F12
  • 11N75