Elliptic curves with a rational point of finite order.
Elliptic curves with bounded ranks in function field towers
Empilements de sphères
Equivalences between elliptic curves and real quadratic congruence function fields
In 1994, the well-known Diffie-Hellman key exchange protocol was for the first time implemented in a non-group based setting. Here, the underlying key space was the set of reduced principal ideals of a real quadratic number field. This set does not possess a group structure, but instead exhibits a so-called infrastructure. More recently, the scheme was extended to real quadratic congruence function fields, whose set of reduced principal ideals has a similar infrastructure. As always, the security...
Erratum: "On the number of prime divisors of the order of elliptic curves modulo p" (Acta Arith. 117 (2005), 341-352)
Estimating isogenies on elliptic curves.
Étude de la courbe elliptique et monogénéité de certains anneaux d’entiers
Euler's concordant forms
Experimental study of the rank of families of elliptic curves over . (Étude expérimentale du rang de familles de courbes elliptiques sur .)
Explicit 4-descents on an elliptic curve
Explicit -descent for elliptic curves in characteristic
Explicit p-adic theta function.
Families of elliptic curves with genus 2 covers of degree 2.
We study genus 2 covers of relative elliptic curves over an arbitrary base in which 2 is invertible. Particular emphasis lies on the case that the covering degree is 2. We show that the data in the "basic construction" of genus 2 covers of relative elliptic curves determine the cover in a unique way (up to isomorphism).A classical theorem says that a genus 2 cover of an elliptic curve of degree 2 over a field of characteristic ≠ 2 is birational to a product of two elliptic curves over the projective...
Fields of Large Transcendence Degree Generated by Values of Elliptic Functions.
Fonctions -adiques à deux variables et -extensions
Formal Groups and Zeta-Functions of Elliptic Curves.
Formes linéaires de logarithmes de points algébriques sur une courbe elliptique de type
Nous obtenons une minoration d’une forme linéaire de logarithmes elliptiques de points algébriques d’une courbe elliptique à multiplication complexe définie sur . Cette minoration est optimale (à constante près) en la hauteur de la forme linéaire considérée.
Fourier-Mukai transforms and stable bundles on elliptic curves.
From holonomy of the Ising model form factors to -fold integrals and the theory of elliptic curves.
From the elliptic regulator to exotic relations.