Ergodic properties of visible lattice points

By Michael Baake, Christian Huck. 2015

54 citations recorded by the source corpus.

Recently, the dynamical and spectral properties of square-free integers, visible lattice points and various generalisations have received increased attention. One reason is the connection of one-dimensional examples such as ℬ-free numbers with Sarnak’s conjecture on the “randomness” of the Möbius function; another is the explicit computability of correlation functions as well as eigenfunctions for these systems together with intrinsic ergodicity properties. Here, we summarise some of the results, with focus on spectral and dynamical aspects, and expand a little on the implications for mathematical diffraction theory.

Subfields: Algebra and Number Theory, Materials Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/99e9977d118258875c0168a4f5681aead8e742a9

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In Algebra and Number Theory

1. J. Kułaga-Przymus
2. Gerhard Keller
3. Mariusz Lemanczyk
4. Sébastien Ferenczi
5. Christoph Richard

In Materials Chemistry

1. J. Kułaga-Przymus
2. Gerhard Keller
3. Mariusz Lemanczyk
4. Sébastien Ferenczi
5. Christoph Richard

In Mathematical Physics

1. J. Kułaga-Przymus
2. Gerhard Keller
3. Mariusz Lemanczyk
4. Sébastien Ferenczi
5. Christoph Richard
6. C. Liverani

Citations in the corpus

• Dynamics on the graph of the torus parametrization (2015, methodology): “This set was identified before in [45], see also [34, 4].”
• Sarnak’s Conjecture: What’s New (2017, methodology): “• Baake and Huck in their survey [13] considered B-free lattice points FB “ FBpΛq :“ Λz Ť bPB bΛ.”