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 be a newform of even weight , level and character and let be a newform of even weight , level and character . We give a generalization of a theorem of Elliott, regarding the average values of Dirichlet -functions, in the context of twisted modular -functions associated to and . Using this result, we find a lower bound in terms of for the number of primitive Dirichlet characters modulo prime whose twisted product -functions are non-vanishing at a fixed point with .

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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

Email:
akbary@cs.uleth.ca

DOI:
https://doi.org/10.1090/S0002-9939-06-08369-9

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.