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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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L-series with nonzero central critical value
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by Kevin James PDF
J. Amer. Math. Soc. 11 (1998), 635-641 Request permission

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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Additional 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