Asymptotic Behavior of Beta-Integers

L. Balková 1 J.-P. Gazeau 2 E. Pelantová
2 APC - THEORIE
Institut für theoretische Physik, APC - UMR 7164 - AstroParticule et Cosmologie
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.
Type de document :
Article dans une revue
Letters in Mathematical Physics, Springer Verlag, 2008, 84, pp.179-198. <10.1007/s11005-008-0241-z>


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Soumis le : mercredi 29 février 2012 - 14:41:37
Dernière modification le : mardi 11 octobre 2016 - 13:25:51

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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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