2018/12/19 by Vávra, Tomáš
#11A63 #11K16 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1812.08228
We prove that all algebraic bases β allow an eventually periodic representations of the elements of \mathbb Q(β) with a finite alphabet of digits \mathcal A. Moreover, the classification of bases allowing that those representations have the so-called weak greedy property is given. The decision problem whether a given pair (β,\mathcal A) allows eventually periodic representations proves to be rather hard, for it is equivalent to a topological property of the attractor of an iterated function system.