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
Consecutive square-free values of the type ,
We show that for any given integer there exist infinitely many consecutive square-free numbers of the type , . We also establish an asymptotic formula for such that , are square-free. The method we used in this paper is due to Tolev.
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
Criterion for 3 to be eleventh power
Cubic norms represented by quadratic sequences
Cyclotomy of order 15 over , (mod 15).
Dedekind cotangent sums
Dedekind Sums and Class Numbers.
Density theorems for exceptional eigenvalues of the Laplacian for congruence groups