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.


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