Linear equations with the Euler totient function
Links between and character sums
We express , as defined in the title, for and prime in terms of values of characters modulo . Using this, we show that the universal lower bound for can, in general, be substantially improved when is composed of primes lying in a fixed residue class modulo . We also prove a corresponding improvement when is the product of the first s primes for infinitely many natural numbers .
Local behaviour of a class of multiplicative functions
Local problems with primes I.
Loi de répartition moyenne des diviseurs des entiers friables
In this paper we consider an extension to friable integers of the arcsine law for the mean distribution of the divisors of integers, originally due to Deshouillers, Dress and Tenenbaum.We describe the limit law and show that it departs from the arcsine law when the friability parameter increases. More precisely, as , the mean distribution shifts from the arcsine law towards Gaussian behaviour.
Lois de répartition des diviseurs.
Lois de répartition des diviseurs
Lois de répartition des diviseurs, 2
Lois de répartition des diviseurs, 3
Lois de répartition des diviseurs. IV
Soit un sous-intervalle de ; on montre que la probabilité pour qu’un diviseur d’un entier appartiennent à possède une loi de distribution dont la mesure de répartition est atomique, à support inclus dans l’ensemble des nombres dyadiques.
Long gaps between deficient numbers
Lower and upper bounds for the number of solutions of
Lower bounds for a certain class of error functions
Lower bounds for expressions of large sieve type
We show that the large sieve is optimal for almost all exponential sums.
Lower bounds for sums of Barban-Davenport-Halberstam type.
Lower Bounds for Sums of Barban-Davenport-Halberstam Type (supplement).