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

Authors:	Xiaotie She

Institution:	Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802

Abstract:	Let be a normalised new form of weight for $\Gamma _{0} (N)$ over ${\mathbb{Q}}$ and , 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 -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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