Ergodic Properties of k-Free Integers in Number Fields
نویسندگان
چکیده
Let K/Q be a degree d extension. Inside the ring of integers OK we define the set of k-free integers Fk and a natural OK-action on the space of binary OK-indexed sequences, equipped with an OK-invariant probability measure associated to Fk. We prove that this action is ergodic, has pure point spectrum, and is isomorphic to a Zdaction on a compact abelian group. In particular, it is not weakly mixing and has zero measure-theoretical entropy. This work generalizes the work of Cellarosi and Sinai [J. Eur. Math. Soc. (JEMS) 15 (2013), no. 4, 1343–1374] that considered the case K = Q and k = 2.
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