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Beta-expansions of rational numbers in quadratic Pisot bases

Publikace na Matematicko-fyzikální fakulta |
2018

Tento text není v aktuálním jazyce dostupný. Zobrazuje se verze "en".Abstrakt

We study rational numbers with purely periodic Rényi β -expansions. For bases β satisfying β 2 =aβ+b with b dividing a , we give a necessary and sufficient condition for γ(β)=1 , i.e., that all rational numbers p/qELEMENT OF[0,1) with gcd(q,b)=1 have a purely periodic β -expansion.

A simple algorithm for determining the value of γ(β) for all quadratic Pisot numbers β is described.