# Ergodic properties of square-free numbers

Francesco Cellarosi; Jakov G. Sinaj

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 4, page 1343-1374
- ISSN: 1435-9855

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topCellarosi, Francesco, and Sinaj, Jakov G.. "Ergodic properties of square-free numbers." Journal of the European Mathematical Society 015.4 (2013): 1343-1374. <http://eudml.org/doc/277274>.

@article{Cellarosi2013,

abstract = {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.},

author = {Cellarosi, Francesco, Sinaj, Jakov G.},

journal = {Journal of the European Mathematical Society},

keywords = {square-free numbers; correlation functions; dynamical systems with pure point spectrum; ergodicity; square-free numbers; correlation functions; dynamical systems with pure point spectrum; ergodicity},

language = {eng},

number = {4},

pages = {1343-1374},

publisher = {European Mathematical Society Publishing House},

title = {Ergodic properties of square-free numbers},

url = {http://eudml.org/doc/277274},

volume = {015},

year = {2013},

}

TY - JOUR

AU - Cellarosi, Francesco

AU - Sinaj, Jakov G.

TI - Ergodic properties of square-free numbers

JO - Journal of the European Mathematical Society

PY - 2013

PB - European Mathematical Society Publishing House

VL - 015

IS - 4

SP - 1343

EP - 1374

AB - 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.

LA - eng

KW - square-free numbers; correlation functions; dynamical systems with pure point spectrum; ergodicity; square-free numbers; correlation functions; dynamical systems with pure point spectrum; ergodicity

UR - http://eudml.org/doc/277274

ER -

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