On the non-vanishing of cubic twists

of automorphic -series

Author:
Xiaotie She

Journal:
Trans. Amer. Math. Soc. **351** (1999), 1075-1094

MSC (1991):
Primary 11F66; Secondary 11F70, 11M41, 11N75

DOI:
https://doi.org/10.1090/S0002-9947-99-02082-6

MathSciNet review:
1451616

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a normalised new form of weight for over and , its base change lift to . A sufficient condition is given for the nonvanishing at the center of the critical strip of infinitely many cubic twists of the -function of . There is an algorithm to check the condition for any given form. The new form of level 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:
https://doi.org/10.1090/S0002-9947-99-02082-6

Received by editor(s):
September 27, 1996

Received by editor(s) in revised form:
February 14, 1997

Article copyright:
© Copyright 1999
American Mathematical Society