A character-sum estimate and applications
A consequence of an effective form of the abc-conjecture
T. Cochrane and R. E. Dressler [CD] proved that the abc-conjecture implies that, for every > 0, the gap between two consecutive numbers A with two exceptions given in Table 2.
A generalization of the Buchstab equation.
A note on numbers with a large prime factor III
A note on sums of powers which have a fixed number of prime factors.
A variant of Selberg's asymptotic formula.
Addendum to Ramachandra's paper "Some problems of analytic number theory, I"
An interval result for the number field v(x,y) function.
Appendix on return-time sequences
Applications des entiers à diviseurs denses
Arithmetic progressions, prime numbers, and squarefree integers
In this paper we establish the distribution of prime numbers in a given arithmetic progression for which is squarefree.
Arithmetical semigroups II: sieving by large and small prime elements. Sets of multiples.
Arithmetical Semigroups III: Elements With Prime Factors in Residue Classes.
Asymptotic aspects of the Diophantine equation
Asymptotic formulae concerning arithmetical functions defined by cross-convolutions. VI: --free integers.
Bemerkung zu der Arbeit von Herrn H. Bekic.
?ber die Anzahl der Zahlen a2 + b2 in einer arithmetischen Reihe gro?er Differenz.
Bornes effectives pour certaines fonctions concernant les nombres premiers
Si est le k nombre premier, la fonction de Chebyshev. Nous obtenons de nouvelles estimations et des améliorations des bornes données par Rosser et Schoenfeld, Schoenfeld et Robin pour les fonctionsCes estimations sont obtenues en utilisant des méthodes basées sur l’intégrale de Stieltjes et par calcul direct pour les petites valeurs.
Bounds for the density of abundant integers.
Carmichael numbers composed of primes from a Beatty sequence
Let α,β ∈ ℝ be fixed with α > 1, and suppose that α is irrational and of finite type. We show that there are infinitely many Carmichael numbers composed solely of primes from the non-homogeneous Beatty sequence . We conjecture that the same result holds true when α is an irrational number of infinite type.