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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the non-vanishing of cubic twists
of automorphic $L$-series


Author: Xiaotie She
Journal: Trans. Amer. Math. Soc. 351 (1999), 1075-1094
MSC (1991): Primary 11F66; Secondary 11F70, 11M41, 11N75
MathSciNet review: 1451616
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $f$ be a normalised new form of weight $2$ for $\Gamma _{0} (N)$ over ${\mathbb{Q}}$ and $F$, its base change lift to $\mathbb{Q}(\sqrt {-3})$. A sufficient condition is given for the nonvanishing at the center of the critical strip of infinitely many cubic twists of the $L$-function of $F$. There is an algorithm to check the condition for any given form. The new form of level $11$ is used to illustrate our method.


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Additional Information

Xiaotie She
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Address at time of publication: Financial Data Planning Corp., 2140 S. Dixie Hwy., Miami, Florida 33133
Email: xiaoties@fdpcorp.com

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02082-6
PII: S 0002-9947(99)02082-6
Received by editor(s): September 27, 1996
Received by editor(s) in revised form: February 14, 1997
Article copyright: © Copyright 1999 American Mathematical Society