Special values of 𝐿-series

Hatcher, Rhonda L.

doi:10.1090/S0002-9939-1992-1068124-1

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Special values of $L$-series
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by Rhonda L. Hatcher PDF

Proc. Amer. Math. Soc. 114 (1992), 337-343 Request permission

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

Heights and the special values of

-series

Benedict H. Gross and Don B. Zagier, Heegner points and derivatives of $L$-series, Invent. Math. 84 (1986), no. 2, 225–320. MR 833192, DOI 10.1007/BF01388809
Rhonda Lee Hatcher, Heights and $L$-series, Canad. J. Math. 42 (1990), no. 3, 533–560. MR 1062744, DOI 10.4153/CJM-1990-028-x