On the density of shifted primes with large prime factors View Full Text


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Article Info

DATE

2018-01

AUTHORS

Bin Feng, Jie Wu

ABSTRACT

As usual, denote by P(n) the largest prime factor of the integer n ⩾ 1 with the convention P(1) = 1. For 0 < θ < 1, define Tθ(x):=|{p≤x:P(p−1)≥pθ}|. In this paper, we obtain a new lower bound for Tθ(x) as x → ∞, which improves some recent results of Luca et al. (2015) and of Chen and Chen (2017). As a corollary, we partially prove a conjecture of Chen and Chen (2017) about the size of Tθ(x). More... »

PAGES

83-94

References to SciGraph publications

  • 1996. The Brun-Titchmarsh Theorem on average in ANALYTIC NUMBER THEORY
  • 1985-06. Théorème de Brun-Titchmarsh; application au théorème de Fermat in INVENTIONES MATHEMATICAE
  • 1973-03. Über die mittlere Verteilung der Werte zahlentheoretischer Funktionen auf Restklassen. I in MATHEMATISCHE ANNALEN
  • 2017-03. On the largest prime factor of shifted primes in ACTA MATHEMATICA SINICA, ENGLISH SERIES
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11425-016-9065-7

    DOI

    http://dx.doi.org/10.1007/s11425-016-9065-7

    DIMENSIONS

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