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

For an elliptic curve E over 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-adicL-function associated toE. 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. Mathematics Subject Classification (2010). 11G40, 11F33.