Publication at Faculty of Mathematics and Physics |
2018
Abstract
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.