The book surveys some recent developments in the arithmetic of modular elliptic curves. It
places a special emphasis on the construction of rational points on elliptic curves, the Birch …

This article describes a conjectural p-adic analytic construction of global points on (modular)
elliptic curves, points which are defined over the ring class fields of real quadratic fields. The …

We construct the three-variable $ p $-adic triple product $ L $-functions attached to Hida
families of elliptic newforms and prove the explicit interpolation formulae at all critical …

Iwasawa's Main Conjecture for Elliptic Curves over Anticyclotomic Z_p-Extensions
Page 1 Annals of Mathematics, 162 (2005), 1-64 Iwasawa's Main Conjecture for elliptic …

The purpose of the paper is to extend and refine earlier results of the author on
nonvanishing of the L-functions associated to modular forms in the anticyclotomic tower of …

Si M est un motif défini sur un corps de nombres, on sait lui associer (au moins
conjecturalement) une fonction analytique complexe L (M, s) définie par un produit eulérien …

We propose a refined version of the Beilinson–Bloch conjecture for the motive associated
with a modular form of even weight. This conjecture relates the dimension of the image of …

Let $ E $ be a quadratic extension of a totally real number field. We construct Stickelberger
elements for Hilbert modular forms of parallel weight 2 in anticyclotomic extensions of $ E …

The arithmetic theory of elliptic curves enters the new century with some of its major secrets
intact. Most notably, the Birch and Swinnerton-Dyer conjecture, which relates the arithmetic …

Teitelbaum formulated a conjecture relating first derivatives of the Mazur-Swinnerton-Dyer p-
adic L-functions attached to modular forms of even weight k≥ 2 to certain [inline-graphic …