Sets of integers and quasi-integers with pairwise common divisor
Sets of integers with pairwise common divisor and a factor from a specified set of primes
Shifted primes without large prime factors
Sieving by Large Prime Factors.
Small gaps in coefficients of -functions and -free numbers in short intervals.
Smooth solutions to the equation: the Conjecture
This paper studies integer solutions to the equation in which none of have a large prime factor. We set , and consider primitive solutions () having no prime factor larger than , for a given finite . We show that the Conjecture implies that for any fixed the equation has only finitely many primitive solutions. We also discuss a conditional result, showing that the Generalized Riemann hypothesis (GRH) implies that for any fixed the equation has infinitely many primitive solutions....
Sommes sans grand facteur premier
Sparsely totient numbers
Square-free values of the Carmichael function.
Square-full divisors of square-full integers.
Sums and differences of power-free numbers
We employ a generalised version of Heath-Brown's square sieve in order to establish an asymptotic estimate of the number of solutions a, b ∈ ℕ to the equations a + b = n and a - b = n, where a is k-free and b is l-free. This is the first time that this problem has been studied with distinct powers k and l.
Sums of nonnegative multiplicative functions over integers without large prime factors II
Sums of nonnegative multiplicative functions over integers without large prime factors I
Sums of some multiplicative functions over a special set of integers
Sums of two relatively prime cubes
Sumsets avoiding squarefree integers
Sur des formules de Atle Selberg
Sur la densité de certains ensembles de multiples, 1
Sur la densité de certains ensembles de multiples, 2
Sur la fonction plus grand facteur premier