beta-expansions and ultimately periodic representations Michel Rigo, Wolfgang Steiner To cite this version: Michel Rigo, Wolfgang Steiner. Abstract beta-expansions and ultimately periodic representations. Journal de Théorie des Nombres de Bordeaux, Société Arithmétique de Bordeaux, 2005, 17, pp.283-299. HAL Id: hal-00023235 https://hal.archives-ouvertes.fr/hal-00023235 Submitted on 21 Apr 2006 ...