Ergodic properties of square-free numbers

F. Cellarosi, Ya G. Sinai

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We construct a natural invariant measure concentrated on the set of square-free numbers, and invariant under the shift. We prove that the corresponding dynamical system is isomorphic to a translation on a compact Abelian group. This implies that this system is not weakly mixing and has zero measure-theoretical entropy.

Original languageEnglish (US)
Pages (from-to)1343-1374
Number of pages32
JournalJournal of the European Mathematical Society
Issue number4
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Correlation functions
  • Dynamical systems with pure point spectrum
  • Ergodicity
  • Square-free numbers


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