Journal of the European Mathematical Society
Full-Text PDF (515 KB) | Metadata | Table of Contents | JEMS summary
Published online: 2013-05-09
Ergodic properties of square-free numbersFrancesco Cellarosi and Yakov G. Sinai (1) University of Illinois at Urbana-Champaign, USA
(2) Princeton University, United States
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.
Keywords: Square-free numbers, correlation functions, dynamical systems with pure point spectrum, ergodicity
Cellarosi Francesco, Sinai Yakov: Ergodic properties of square-free numbers. J. Eur. Math. Soc. 15 (2013), 1343-1374. doi: 10.4171/JEMS/394