L-series with nonzero central critical value

James, Kevin

doi:10.1090/S0894-0347-98-00263-X

L-series with nonzero central critical value
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by Kevin James

J. Amer. Math. Soc. 11 (1998), 635-641

DOI: https://doi.org/10.1090/S0894-0347-98-00263-X

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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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