Geodesic
Ergodic properties of visible lattice points
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and applications, Tome 288 (2015), pp. 184-208

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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 $\mathscr B$-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. 
@article{TM_2015_288_a12,
     author = {Michael Baake and Christian Huck},
     title = {Ergodic properties of visible lattice points},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {184--208},
     publisher = {mathdoc},
     volume = {288},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2015_288_a12/}
}
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Michael Baake; Christian Huck. Ergodic properties of visible lattice points. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and applications, Tome 288 (2015), pp. 184-208. http://geodesic.mathdoc.fr/item/TM_2015_288_a12/