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.