Simultaneous visibility in the integer lattice

Daniel Berend, Rishi Kumar, Andrew Pollington

Research output: Contribution to journalArticlepeer-review


Two lattice points are visible from one another if there is no lattice point on the open line segment joining them. Let S be a finite subset of Zk. The asymptotic density of the set of lattice points, visible from all points of S, was studied by several authors. Our main result is an improved upper bound on the error term. We also find the Schnirelmann density of the set of visible points from some sets S. Finally, we discuss these questions from the point of view of ergodic theory.

Original languageEnglish
Pages (from-to)84-123
Number of pages40
JournalJournal of Number Theory
StatePublished - 1 Sep 2023


  • Schnirelmann densities
  • Selberg's sieve
  • Simultaneous visibility
  • Unique ergodicity

ASJC Scopus subject areas

  • Algebra and Number Theory


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