Elliptic units of cyclic unramified extensions of complex quadratic fields
Embedding orders into central simple algebras
The question of embedding fields into central simple algebras over a number field was the realm of class field theory. The subject of embedding orders contained in the ring of integers of maximal subfields of such an algebra into orders in that algebra is more nuanced. The first such result along those lines is an elegant result of Chevalley [6] which says that with the ratio of the number of isomorphism classes of maximal orders in into which the ring of integers of can be embedded...
Ensembles de Julia et propriétés de localisation des entiers algbériques.
Ensembles de nombres algébriques et transformations rationnelles
Ensembles d’unicité dans des produits de corps -adiques
Ensembles fermés de nombres algébriques
Ensembles fermés de nombres algébriques
Ensembles fermés de nombres algébriques
Ensembles fermés d'entiers algébriques
Entiers algébriques dont les conjugués sont proches du cercle unité
Enumerating non-equivalent matrices over principal ideal domains
Enumerating quartic dihedral extensions of with signatures
In a previous paper, we have given asymptotic formulas for the number of isomorphism classes of -extensions with discriminant up to a given bound, both when the signature of the extensions is or is not specified. We have also given very efficient exact formulas for this number when the signature is not specified. The aim of this paper is to give such exact formulas when the signature is specified. The problem is complicated by the fact that the ray class characters which appear are not all genus characters....
Equations for Mahler measure and isogenies
We study some functional equations between Mahler measures of genus-one curves in terms of isogenies between the curves. These equations have the potential to establish relationships between Mahler measure and especial values of -functions. These notes are based on a talk that the author gave at the “Cuartas Jornadas de Teoría de Números”, Bilbao, 2011.
Equations in roots of unity
Equidistribution and the heights of totally real and totally p-adic numbers
C. J. Smyth was among the first to study the spectrum of the Weil height in the field of all totally real numbers, establishing both lower and upper bounds for the limit infimum of the height of all totally real integers, and determining isolated values of the height. Later, Bombieri and Zannier established similar results for totally p-adic numbers and, inspired by work of Ullmo and Zhang, termed this the Bogomolov property. In this paper, we use results on equidistribution of points of low height...
Equidistribution in -arithmetic and adelic spaces
We give an introduction to adelic mixing and its applications for mathematicians knowing about the mixing of the geodesic flow on hyperbolic surfaces. We focus on the example of the Hecke trees in the modular surface.
Equidistribution of Frobenius classes and the volumes of tubes
Équirépartition dans les adèles
Équirépartition modulo dans un corps de séries formelles sur un corps fini
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...