Caractères quadratiques de groupes abéliens finis et sommes de Gauss
Character Sums and Primitive Roots in Algebraic Number Fields.
Character sums and products of factorials modulo
In this paper, we apply character sum estimates to study products of factorials modulo .
Character sums and Ramsey properties of generalized Paley graphs.
Character sums in complex half-planes
Let be a finite subset of an abelian group and let be a closed half-plane of the complex plane, containing zero. We show that (unless possesses a special, explicitly indicated structure) there exists a non-trivial Fourier coefficient of the indicator function of which belongs to . In other words, there exists a non-trivial character such that .
Character sums in finite fields
Characterization of the torsion of the Jacobians of two families of hyperelliptic curves
Consider the families of curves and where A is a nonzero rational. Let and denote their respective Jacobian varieties. The torsion points of and are well known. We show that for any nonzero rational A the torsion subgroup of is a 2-group, and for A ≠ 4a⁴,-1728,-1259712 this subgroup is equal to (for a excluded values of A, with the possible exception of A = -1728, this group has a point of order 4). This is a variant of the corresponding results for (A ≠ 4) and . We also almost...
Cohomologie des fonctions
Computing higher rank primitive root densities
We extend the "character sum method" for the computation of densities in Artin primitive root problems given by Lenstra and the authors to the situation of radical extensions of arbitrary rank. Our algebraic set-up identifies the key parameters of the situation at hand, and obviates the lengthy analytic multiplicative number theory arguments that used to go into the computation of actual densities. It yields a conceptual interpretation of the formulas obtained, and enables us to extend their range...
Computing the Volume, Counting Integral Points, and Exponential Sums.
Conditional bounds for small prime solutions of linear equations.
Conditions suffisantes d’équirépartition modulo 1 de suites et
Congruence properties of the hyperkloosterman sum
Correction to "Minimal polynomials for Gauss periods with f=2" (Acta Arith. 121 (2006), 233-257)
Corrigendum to "An improvement on Olson's constant for ℤₚ ⊕ ℤₚ" (Acta Arith. 141 (2010), 311-319)
Corrigendum to the paper "Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory"
Counting with Gauss' sums.
Crible asymptotique et sommes de Kloosterman
On montre à l’aide de méthodes de crible, de méthodes issues de la théorie des formes automorphes et de géométrie algébrique ainsi qu’à l’aide de la loi de Sato-Tate verticale que le signe des sommes de Kloosterman change une infinité de fois pour parcourant les entiers sans facteur carré ayant au plus facteurs premiers. Ceci améliore un résultat précédent de Fouvry et Michel qui avaient obtenu à la place de .
Crible étrange et sommes de Kloosterman
Critère de reconnaissabilité de fonctions analytiques et fonctions entières arithmétiques