Clusters of primes with square-free translates

• Roger C. Baker ^[1] ; Paul Pollack ^[2]
  1. [1] Brigham Young University

     Brigham Young University

     Estados Unidos

     
  2. [2] University of Georgia

     University of Georgia

     Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 33, Nº 3, 2017 (Ejemplar dedicado a: Yves Meyer), págs. 809-829
• Idioma: inglés
• DOI: 10.4171/RMI/956
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let R be a finite set of integers satisfying appropriate local conditions. We show the existence of long clusters of primes p in bounded length intervals with p−b squarefree for all b∈R. Moreover, we can enforce that the primes p in our cluster satisfy any one of the following conditions: (1) p lies in a short interval [N,N+N7/12+ϵ], (2) p belongs to a given inhomogeneous Beatty sequence, (3) with c∈(8/9,1) fixed, pc lies in a prescribed interval mod 1 of length p−1+c+ϵ.