Clusters of primes with square-free translates

  • Roger C. Baker

    Brigham Young University, Provo, USA
  • Paul Pollack

    University of Georgia, Athens, USA

Abstract

Let be a finite set of integers satisfying appropriate local conditions. We show the existence of long clusters of primes in bounded length intervals with squarefree for all . Moreover, we can enforce that the primes in our cluster satisfy any one of the following conditions: (1) lies in a short interval , (2) belongs to a given inhomogeneous Beatty sequence, (3) with fixed, lies in a prescribed interval mod of length .

Cite this article

Roger C. Baker, Paul Pollack, Clusters of primes with square-free translates. Rev. Mat. Iberoam. 33 (2017), no. 3, pp. 809–829

DOI 10.4171/RMI/956