Rational base number systems for \(p\)-adic numbers (Q2911429)

This paper is concerned with rational base number systems for \(p\)-adic numbers, in particular with those introduced in [\textit{S. Akiyama} et al., Isr. J. Math. 168, 53--91 (2008; Zbl 1214.11089)]. The authors identify those numbers which have finite and eventually periodic representations, and they determine the number of representations of a given \(p\)-adic number. Moreover, the authors investigate the relation between this number system and three other rational base number systems for \(p\)-adic numbers, and show that they all are in some sense isomorphic and share most of their properties.