The k-tuple jumping champions among consecutive primes
The least prime in an arithmetic progression with prime difference.
The least square-free number in an arithmetic progression.
The localisation of primes in arithmetic progressions of irrational modulus
A new method for counting primes in a Beatty sequence is proposed, and it is shown that an asymptotic formula can be obtained for the number of such primes in a short interval.
The mean behavior of primes in arithmetic progressions.
The -th prime asymptotically
A new derivation of the classic asymptotic expansion of the -th prime is presented. A fast algorithm for the computation of its terms is also given, which will be an improvement of that by Salvy (1994).Realistic bounds for the error with , after having retained the first terms, for , are given. Finally, assuming the Riemann Hypothesis, we give estimations of the best possible such that, for , we have where is the sum of the first four terms of the asymptotic expansion.
The number of k-ary divisors of a generalized integer
The number of k-free and k-ary divisors of m which are prime to n.
The number of prime factors of binomial coefficients
The number of primes in a short interval.
The prime number theorem for Beurling's generalized numbers. New cases
The quickest proof of the prime number theorem
The sequences of prime divisors of integers
The Siegel-Walfisz theorem for Rankin-Selberg L-functions associated with two cusp forms
The Square Sieve and Consecutive Square-Free Numbers.
Théorème de Fermat : la contribution de Fouvry
Théorème des nombres premiers pour les fonctions digitales
The aim of this work is to estimate exponential sums of the form , where Λ denotes von Mangoldt’s function, f a digital function, and β ∈ ℝ a parameter. This result can be interpreted as a Prime Number Theorem for rotations (i.e. a Vinogradov type theorem) twisted by digital functions.
Trigonometrische Reihen über multiplikativen Zahlenmengen.