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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the non-vanishing of cubic twists of automorphic $L$-series
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by Xiaotie She PDF
Trans. Amer. Math. Soc. 351 (1999), 1075-1094 Request permission

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
  • Received by editor(s): September 27, 1996
  • Received by editor(s) in revised form: February 14, 1997
  • © Copyright 1999 American Mathematical Society
  • 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