Remark on the minimum discriminant of normal fields
Remarks on factorizations in algebraic number fields
Remarks on normal bases
We prove that any Galois extension of a commutative ring with a normal basis and abelian Galois group of odd order has a self-dual normal basis. We apply this result to get a very simple proof of nonexistence of normal bases for certain extensions which are of interest in number theory.
Remarks on the number of non-zero coefficients of polynomials.
Remarks on the λₚ-invariants of cyclic fields of degree p
Remarks on Unit indices of imaginary abelian number fields.
Remarks on unit indices of imaginary abelian number fields II.
Remarks on Weil’s quadratic functional in the theory of prime numbers, I
This Memoir studies Weil’s well-known Explicit Formula in the theory of prime numbers and its associated quadratic functional, which is positive semidefinite if and only if the Riemann Hypothesis is true. We prove that this quadratic functional attains its minimum in the unit ball of the -space of functions with support in a given interval , and prove again Yoshida’s theorem that it is positive definite if is sufficiently small. The Fourier transform of the functional gives rise to a quadratic...
Remarques sur la structure galoisienne des unités des corps de nombres
Remarques sur le groupe de classes du composé de deux corps de nombres linéairement disjoints
Remarques sur les différentielles des polylogarithmes uniformes
On étudie des équations fonctionnelles pour les différentielles des polylogarithmes uniformes. Un des ingrédients est l’analogue infinitésimal d’un complexe introduit par Goncharov. On obtient en particulier une équation fonctionnelle à 22 termes pour la différentielle du trilogarithme.
Remarques sur les nombres de Pisot-Vijayaraghavan
Remarques sur l'invariant mu d'Iwasawa dans le cas CM
Répartition de dans les adèles
Répartition modulo 1 dans un corps de séries formelles sur un corps fini [Book]
Representability by certain norm forms over algebraic number fields
Representation fields for commutative orders
A representation field for a non-maximal order in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of . Not every non-maximal order has a representation field. In this work we prove that every commutative order has a representation field and give a formula for it. The main result is proved for central simple algebras over arbitrary global fields.
Representation fields for cyclic orders
Representation of a prime as the sum of squares in a tower of fields.
Representation of prime powers in arithmetical progressions by binary quadratic forms
Let be a set of binary quadratic forms of the same discriminant, a set of arithmetical progressions and a positive integer. We investigate the representability of prime powers lying in some progression from by some form from .