Journal of the American Mathematical Society

Author(s): Kevin James
Journal: J. Amer. Math. Soc. 11 (1998), 635-641.
MSC (1991): Primary 11G40
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Abstract: Given a cusp form $f$

of even integral weight and its associated $L$

-function

, 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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