A Birch and Swinnerton-Dyer conjecture for the Mazur-Tate

circle pairings

(Un exposé de Massimo Bertolini au séminaire de théorie des nombres de Chevaleret le 2 décembre 2002)

Résumé :

The talk discusses work in progress (with Henri Darmon) on
the study of an analogue of the Birch and Swinnerton-Dyer conjecture for the
Mazur-Tate circle pairing attached to a modular elliptic curve. This work
relates the circle pairing to a generalized period integral of the cusp form
associated to the elliptic curve.