PSL septimic fields with a power basis
We give an infinite set of distinct monogenic septimic fields whose normal closure has Galois group .
Quelques fonctions moyenne-périodiques bornées
Quelques remarques sur le cas sauvage.
Relations d'inégalités effectives en théorie algébrique des nombres
Relative Bogomolov extensions
A subfield K ⊆ ℚ̅ has the Bogomolov property if there exists a positive ε such that no non-torsion point of has absolute logarithmic height below ε. We define a relative extension L/K to be Bogomolov if this holds for points of . We construct various examples of extensions which are and are not Bogomolov. We prove a ramification criterion for this property, and use it to show that such extensions can always be constructed if some rational prime has bounded ramification index in K.
Relative integral basis for algebraic number fields.
Remark on a problem of Schinzel
Representation of a prime as the sum of squares in a tower of fields.
Réseaux sur les anneaux d'entiers algébriques
Résidus de puissances
Résultats de stabilité algébrique.
Résultats récents sur la monogénéité des anneaux d' entiers
Roots of unity in definite quaternion orders
A commutative order in a quaternion algebra is called selective if it embeds into some, but not all, of the maximal orders in the algebra. It is known that a given quadratic order over a number field can be selective in at most one indefinite quaternion algebra. Here we prove that the order generated by a cubic root of unity is selective for any definite quaternion algebra over the rationals with type number 3 or larger. The proof extends to a few other closely related orders.
Rotations sur les groupes, nombres algébriques, et substitutions
Second order strong divisibility sequences in an algebraic number field
Selberg Formulae for Gaussian integers
Semigroup crossed products and Hecke algebras arising from number fields.
Sequences of algebraic integers and density modulo
We prove density modulo of the sets of the formwhere is a pair of rationally independent algebraic integers of degree satisfying some additional assumptions, and is any sequence of real numbers.
Solution des problèmes de Favard
Solution des problèmes de Favard
Pour tout , on calcule un rang tel que tout entier algébrique de degré au moins ait deux conjugués vérifiant . De plus, on donne une nouvelle preuve de l’égalité .