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Proceedings of the American Mathematical Society

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

 
 

 

Simultaneous non-vanishing of twists


Author: Amir Akbary
Journal: Proc. Amer. Math. Soc. 134 (2006), 3143-3151
MSC (2000): Primary 11F67
DOI: https://doi.org/10.1090/S0002-9939-06-08369-9
Published electronically: May 18, 2006
MathSciNet review: 2231896
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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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.