Clusters of primes with square-free translates
Roger C. Baker
Brigham Young University, Provo, USAPaul Pollack
University of Georgia, Athens, USA
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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