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Simultaneous non-vanishing of twists

Author: Amir Akbary
Journal: Proc. Amer. Math. Soc. 134 (2006), 3143-3151
MSC (2000): Primary 11F67
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

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.