Finding almost squares. V.
Fractional and integral parts of
Integer Points Close to a Smooth Curve
∗ This research is partially supported by the Bulgarian National Science Fund under contract MM-403/9We review the existing estimates for the number of integer points close to a smooth curve and improve on some of these.
Integers free of prime divisors from an interval, I
Integers free of prime divisors from an interval, II
Integers with a large friable component
Integers with no large prime factors
Integers without large prime factors
Integers without large prime factors in short intervals and arithmetic progressions
Lattice points in a circle: An improved mean-square asymptotics
Le plus grand facteur premier de n² + 1 où est presque premier
L'ensemble exceptionnel dans la conjecture de Szpiro
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 .
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.
Lower and upper bounds for the number of solutions of
Maximal Sets of Integers with Small Common Divisors.
Méthodes d'optimisation pour un problème de théorie des nombres
Metrical results on sums of squares and prime values of the integer parts of sequences
Minimal Niven numbers
Multiple exponential sums with monomials