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- W1980707902 abstract "Given a rational elliptic curve E, a suitable imaginary quadratic field K and a quaternionic Hecke eigenform g of weight 2 obtained from E by level raising such that the sign in the functional equation for L_K(E,s) (respectively, L_K(g,1)) is -1 (respectively, +1), we prove a ``Jochnowitz congruence'' between the algebraic part of L'_K(E,1) (expressed in terms of Heegner points on Shimura curves) and the algebraic part of L_K(g,1). This establishes a relation between Zhang's formula of Gross-Zagier type for central derivatives of L-series and his formula of Gross type for special values. Our results extend to the context of Shimura curves attached to division quaternion algebras previous results of Bertolini and Darmon for Heegner points on classical modular curves." @default.
- W1980707902 created "2016-06-24" @default.
- W1980707902 creator A5051126408 @default.
- W1980707902 date "2014-08-14" @default.
- W1980707902 modified "2023-10-16" @default.
- W1980707902 title "Heegner points and Jochnowitz congruences on Shimura curves" @default.
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- W1980707902 doi "https://doi.org/10.1090/s0002-9939-2014-12188-5" @default.
- W1980707902 hasPublicationYear "2014" @default.
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