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 …

À chaque entier k⩾ 2 et chaque L∈ Qp, on associe conjecturalement un espace de Banach
p-adique B (k, L) muni d'une action continue unitaire de GL2 (Qp). On montre que B (k, L) …

Hida families and rational points on elliptic curves Page 1 DOI: 10.1007/s00222-007-0035-4
Invent. math. 168, 371–431 (2007) Hida families and rational points on elliptic curves Massimo …

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 …

In this article, we generalize some works of Bertolini–Darmon and Vatsal on anticyclotomic L-
functions attached to modular forms of weight two to higher weight case. We construct a …

In this paper we prove a Gross-Zagier type formula for the anticyclotomic p-adic L-function of
an elliptic modular form f of higher weight and of multiplicative type at p. For such f we also …

Let f be a modular eigenform of even weight k≥ 2 and new at a prime p dividing exactly the
level with respect to an indefinite quaternion algebra. The theory of Fontaine–Mazur allows …

p-adic L-functions and the Rationality of Darmon Cycles Page 1 Canad. J. Math. Vol. 64 (5),
2012 pp. 1122–1181 http://dx.doi.org/10.4153/CJM-2011-076-8 c Canadian Mathematical …

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 …