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 | References | Similar Articles | Additional Information

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.