Taille des valeurs de fonctions L de carrés symétriques au bord de la bande critique.
Teilerprobleme (Vierte Abhandlung)
Terme d'erreur dans le théorème de la progression arithmétique.
Ternary quadratic forms with rational zeros
We consider the Legendre quadratic formsand, in particular, a question posed by J–P. Serre, to count the number of pairs of integers , for which the form has a non-trivial rational zero. Under certain mild conditions on the integers , we are able to find the asymptotic formula for the number of such forms.
The (ABC) Conjecture and the radical index of integers
The additive complements of primes and Goldbach's problem
We extend two results of Ruzsa and Vu on the additive complements of primes.
The additive divisor problem and its analogs for Fourier coefficients of cusp forms. I.
The appearence of tens of billion of integers x with ... 24, 13 (x) ... 24, 1 (x) in the vicinity of 10 12.
The asymptotic behaviour of the counting functions of Ω-sets in arithmetical semigroups
We consider an axiomatically-defined class of arithmetical semigroups that we call simple L-semigroups. This class includes all generalized Hilbert semigroups, in particular the semigroup of non-zero integers in any algebraic number field. We show, for all positive integers k, that the counting function of the set of elements with at most k distinct factorization lengths in such a semigroup has oscillations of logarithmic frequency and size for some M>0. More generally, we show a result on...
The asymptotic distribution of exponential sums. I.
The asymptotic distribution of exponential sums. II.
The average of the least primitive root modulo
The average order of a class of arithmetic functions over arithmetic progressions with applications to quadratic forms.
The average order of a permutation.
The average order of over integers free of large prime factors
The average order of the Dirichlet series of the gcd-sum function.
The average order of two arithmetical functions
The average orders of Hooley’s -functions, II
The Billiard in a Regular Polygon.
The binary additive divisor problem