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Asymptotic Behavior of Beta-Integers

L. Balková 1 J.-P. Gazeau 2 E. Pelantová
APC (UMR_7164) - AstroParticule et Cosmologie, Institut für theoretische Physik
Abstract : Beta-integers ("β-integers") are those numbers which are the counterparts of integers when real numbers are expressed in an irrational base β > 1. In quasicrystalline studies, β-integers supersede the "crystallographic" ordinary integers. When the number β is a Parry number, the corresponding β-integers realize only a finite number of distances between consecutive elements and are in this sense the most comparable to ordinary integers. In this paper, we point out the similarity of β-integers and ordinary integers in the asymptotic sense, in particular for a subclass of Parry numbers - Pisot numbers for which their Parry and minimal polynomial coincide.
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Submitted on : Wednesday, February 29, 2012 - 2:41:37 PM
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L. Balková, J.-P. Gazeau, E. Pelantová. Asymptotic Behavior of Beta-Integers. Letters in Mathematical Physics, Springer Verlag, 2008, 84, pp.179-198. ⟨10.1007/s11005-008-0241-z⟩. ⟨in2p3-00326547⟩



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