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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Simultaneous non-vanishing of twists
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by Amir Akbary PDF
Proc. Amer. Math. Soc. 134 (2006), 3143-3151 Request permission

Abstract:

Let $f$ be a newform of even weight $k$, level $M$ and character $\psi$ and let $g$ be a newform of even weight $l$, level $N$ and character $\eta$. We give a generalization of a theorem of Elliott, regarding the average values of Dirichlet $L$-functions, in the context of twisted modular $L$-functions associated to $f$ and $g$. Using this result, we find a lower bound in terms of $Q$ for the number of primitive Dirichlet characters modulo prime $q\leq Q$ whose twisted product $L$-functions $L_{f,\chi }(s_0) L_{g,\chi }(s_0)$ are non-vanishing at a fixed point $s_0=\sigma _0+it_0$ with $\frac {1}{2}<\sigma _0\leq 1$.
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Additional Information
  • Amir Akbary
  • Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive West, Lethbridge, Alberta, Canada T1K 3M4
  • MR Author ID: 650700
  • Email: akbary@cs.uleth.ca
  • Received by editor(s): August 16, 2004
  • Received by editor(s) in revised form: June 9, 2005
  • Published electronically: May 18, 2006
  • Additional Notes: This research was partially supported by NSERC
  • Communicated by: Wen-Ching Winnie Li
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3143-3151
  • MSC (2000): Primary 11F67
  • DOI: https://doi.org/10.1090/S0002-9939-06-08369-9
  • MathSciNet review: 2231896