arXiv Open Access 2013

Ergodic Properties of $k$-Free Integers in Number Fields

Francesco Cellarosi Ilya Vinogradov

Lihat Sumber

Abstrak

Let $K/\mathbf Q$ be a degree $d$ extension. Inside the ring of integers $\mathcal O_K$ we define the set of $k$-free integers $\mathcal F_k$ and a natural $\mathcal O_K$-action on the space of binary $\mathcal O_K$-indexed sequences, equipped with an $\mathcal O_K$-invariant probability measure associated to $\mathcal F_k$. We prove that this action is ergodic, has pure point spectrum and is isomorphic to a $\mathbf Z^d$-action on a compact abelian group. In particular, it is not weakly mixing and has zero measure-theoretical entropy. This work generalizes the paper by the first author and Sinai arXiv:1112.4691 [math.DS] where $K=\mathbf Q$ and $k=2$.

Topik & Kata Kunci

math.DS math.NT

Penulis (2)

Francesco Cellarosi

Ilya Vinogradov

Format Sitasi

APA MLA BibTeX

Cellarosi, F., Vinogradov, I. (2013). Ergodic Properties of $k$-Free Integers in Number Fields. https://arxiv.org/abs/1304.0214

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2013
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓