Autour de la conjecture de Sato-Tate pour les sommes de Kloosterman I.
Averages of short exponential sums, II
Binary Kloosterman sums using Stickelberger's theorem and the Gross-Koblitz formula
Character sums and Ramsey properties of generalized Paley graphs.
Conditional bounds for small prime solutions of linear equations.
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)
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
Determination of modulo p
Die galoisschen Gauss΄schen Summen von Hasse
Distribution of difference between inverses of consecutive integers modulo .
Distributional properties of powers of matrices
We apply the larger sieve to bound the number of matrices not having large order when reduced modulo the primes in an interval. Our motivation is the relation with linear recursive congruential generators. Basically our results establish that the probability of finding a matrix with large order modulo many primes drops drastically when a certain threshold involving the number of primes and the order is exceeded. We also study, for a given prime and a matrix, the existence of nearby non-similar...
Ein neuer beweis für die Reziprozitätsformel der Gaußschen Summen in beliebigen algebraischen Zahlkörpern
Estimation of exponential sums of polynomials of higher degrees II
Exponential sums for O¯(2n,q) and their applications
Exponential sums for symplectic groups and their applications
Finding almost squares
Finite projective planes, Fermat curves, and Gaussian periods
One of the oldest and most fundamental problems in the theory of finite projective planes is to classify those having a group which acts transitively on the incident point-line pairs (flags). The conjecture is that the only ones are the Desarguesian projective planes (over a finite field). In this paper, we show that non-Desarguesian finite flag-transitive projective planes exist if and only if certain Fermat surfaces have no nontrivial rational points, and formulate several other equivalences involving...