This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number.
This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number.
In the study of the -adic sum of digits function , the arithmetical function and for plays a very important role. In this paper, we firstly generalize the relation between and to a bijective relation between arithmetical functions. And as an application, we investigate some aspects of the sum of digits functions induced by binary infinite Gray codes . We can show that the difference of the sum of digits function, , is realized by an automaton. And the summation formula of the sum...