Commentarii Mathematici Helvetici


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Volume 86, Issue 4, 2011, pp. 867–945
DOI: 10.4171/CMH/243

Published online: 2011-09-22

Heegner points and p-adic L-functions for elliptic curves over certain totally real fields

Chung Pang Mok[1]

(1) McMaster University, Hamilton, Canada

For an elliptic curve $E$ over $\mathbb{Q}$ satisfying suitable hypotheses, Bertolini and Darmon have derived a formula for the Heegner point on $E$ in terms of the central derivative of the two variable $p$-adic $L$-function associated to $E$. In this paper, we generalize their work to the setting of totally real fields in which $p$ is inert. We also use this generalization to improve the results obtained by Bertolini–Darmon in the case of an elliptic curve defined over the field of rational numbers.

Keywords: Hilbert modular forms, p-adic L-functions, Heegner points

Mok Chung Pang: Heegner points and p-adic L-functions for elliptic curves over certain totally real fields. Comment. Math. Helv. 86 (2011), 867-945. doi: 10.4171/CMH/243