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Heegner points and derivatives of $$L$$-functions. (Points de Heegner et dérivées de fonctions $$L$$.) (French) Zbl 0538.14023
This paper is a summary of the authors’ results on Heegner points of modular curves. These results are intimately connected with the conjecture of Birch and Swinnerton-Dyer. Moreover, together with previous results of Goldfeld, they yield an effective lower bound for class numbers of imaginary quadratic fields.

##### MSC:
 11G40 $$L$$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 11F11 Holomorphic modular forms of integral weight 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 14K15 Arithmetic ground fields for abelian varieties 11R29 Class numbers, class groups, discriminants 11R11 Quadratic extensions