2015/01/01 by Michael Baake, Christian Huck · 27 citations
Materials Science · Mathematics · #Analytic Number Theory Research #Computability #Conjecture #Discrete mathematics #Dynamical systems theory #Eigenfunction #Eigenvalues and eigenvectors #Ergodic theory #Ergodicity #Lattice (music) #Mathematical Dynamics and Fractals #Mathematics #Physics #Pure mathematics #Quantum mechanics #Quasicrystal Structures and Properties #Randomness #Statistical physics #math.DS #msc:11H06 #msc:11R04 #msc:37A35 #msc:37A45 #msc:42A38 #msc:52C07
paper · pdf · doi:10.1134/s0081543815010137
published in Proceedings of the Steklov Institute of Mathematics 288(1), 165-188 (Pleiades Publishing) · 26 pages, 5 figures; results presented at the Mini-Workshop "Dynamical versus Diffraction Spectra in the Theory of Quasicrystals" at the MFO in Oberwolfach in December 2014; revised version with minor corrections
openalex publication_date 2015/01/01 · arxiv created 2015/05/05 · arxiv updated 2015/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.