Codes et formes quadratiques
Co-fibered products of algebraic curves
We give examples of failure of the existence of co-fibered products in the category of algebraic curves.
Cohomologie galoisienne : progrès et problèmes
Complexes de groupes de type multiplicatif et groupe de Brauer non ramifié des espaces homogènes
On calcule par des méthodes arithmétiques le groupe de Brauer non ramifié des espaces homogènes de groupes algébriques linéaires sur différents corps. Les formules obtenues font intervenir l’hypercohomologie de complexes de groupes de type multiplicatif.
Composition of binary quadratic forms
Composition of binary quadratic forms over integral domains
Composition of norm-type forms.
Composition of quaternary quadratic forms
Compositions of quadratic forms with quadratic, bilinear or Hermitian forms.
Computations of cyclotomic lattices.
Computations of Witt Groups of Finite Groups.
Congruence properties of the number of solutions of some equations.
Congruences for and
Congruences for certain families of Apéry-like sequences
We systematically investigate the expressions and congruences for both a one-parameter family as well as a two-parameter family of sequences.
Congruences for
Let ℤ be the set of integers, and let (m,n) be the greatest common divisor of the integers m and n. Let p ≡ 1 (mod 4) be a prime, q ∈ ℤ, 2 ∤ q and p=c²+d²=x²+qy² with c,d,x,y ∈ ℤ and c ≡ 1 (mod 4). Suppose that (c,x+d)=1 or (d,x+c) is a power of 2. In this paper, by using the quartic reciprocity law, we determine in terms of c,d,x and y, where [·] is the greatest integer function. Hence we partially solve some conjectures posed in our previous two papers.
Congruences for representations of primes by binary quadratic forms
Conjugacy, Genus, and Class Numbers.
Conservative Quadratic Forms.
Constructing Quasi-Pythagorean Fields
Construction of entire modular forms of weights 5 and 6 for the congruence group .