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L-series with nonzero central critical value

Author: Kevin James
Journal: J. Amer. Math. Soc. 11 (1998), 635-641
MSC (1991): Primary 11G40
MathSciNet review: 1492854
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Abstract: Given a cusp form $f$ of even integral weight and its associated $L$-function $L(f,s)$, we expect that a positive proportion of the quadratic twists of $L$ will have nonzero central critical value. In this paper we give examples of weight two newforms whose associated $L$-functions have the property that a positive proportion of its quadratic twists have nonzero central critical value.

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Additional Information

Kevin James
Affiliation: Department of Mathematics, Pennsylvania State University, 218 McAllister Building, University Park, Pennsylvania 16802-6401

Received by editor(s): August 13, 1997
Received by editor(s) in revised form: January 20, 1998
Article copyright: © Copyright 1998 American Mathematical Society

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