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Article Dans Une Revue Journal of Number Theory Année : 2020

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].
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Dates et versions

hal-03216054 , version 1 (03-05-2021)

Identifiants

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Jie Wu. ELLIOTT-HALBERSTAM CONJECTURE AND VALUES TAKEN BY THE LARGEST PRIME FACTOR OF SHIFTED PRIMES. Journal of Number Theory, 2020, 206, pp.282-295. ⟨10.1016/j.jnt.2019.06.015⟩. ⟨hal-03216054⟩
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