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Special values of $ L$-series


Author: Rhonda L. Hatcher
Journal: Proc. Amer. Math. Soc. 114 (1992), 337-343
MSC: Primary 11F67; Secondary 11R52
DOI: https://doi.org/10.1090/S0002-9939-1992-1068124-1
MathSciNet review: 1068124
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Abstract: The main result of this paper is an equation representing the value of the Dirichlet series $ L(f,A,s)$ at $ s = k$ in terms of the height pairings of special points on a vector bundle $ V$ associated with the quaternion algebra over $ {\mathbf{Q}}$ ramified at $ N$ and $ \infty $.


References [Enhancements On Off] (What's this?)

  • [1] B. H. Gross, Heights and the special values of $ L$-series, CMS Conf. Proc. 7 (1986).
  • [2] B. H. Gross and D. Zagier, Heegner points and derivatives of $ L$-series, Invent. Math. 84 (1986), 225-320. MR 833192 (87j:11057)
  • [3] R. L. Hatcher, Heights and $ L$-series, Canad. J. Math. 42 (1990), 533-560. MR 1062744 (92b:11031)

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DOI: https://doi.org/10.1090/S0002-9939-1992-1068124-1
Article copyright: © Copyright 1992 American Mathematical Society

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