## 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.## References

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## Bibliographic Information

**Kevin James**- Affiliation: Department of Mathematics, Pennsylvania State University, 218 McAllister Building, University Park, Pennsylvania 16802-6401
- MR Author ID: 629241
- Email: klj@math.psu.edu
- Received by editor(s): August 13, 1997
- Received by editor(s) in revised form: January 20, 1998
- © Copyright 1998 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**11**(1998), 635-641 - MSC (1991): Primary 11G40
- DOI: https://doi.org/10.1090/S0894-0347-98-00263-X
- MathSciNet review: 1492854