ELLIOTT-HALBERSTAM CONJECTURE AND VALUES TAKEN BY THE LARGEST PRIME FACTOR OF SHIFTED PRIMES
Résumé
Denote by P the set of all primes and by P + (n) the largest prime factor of integer n 1 with the convention P + (1) = 1. For each η > 1, let c = c(η) > 1 be some constant depending on η and P a,c,η := {p ∈ P : p = P + (q − a) for some prime q with p η < q c(η)p η }. In this paper, under the Elliott-Halberstam conjecture we prove, for y → ∞, π a,c,η (x) := |(1, x] ∩ P a,c,η | ∼ π(x) or π a,c,η (x) a,η π(x) according to values of η. These complement for some results of Banks-Shparlinski [1], of Wu [12] and of Chen-Wu [2].
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)