A characterization of rational numbers by p-adic Sylvester series expansions
نویسندگان
چکیده
منابع مشابه
Complementary Bell Numbers and p-adic Series
In this article, we generalize a result of Murty on the non-vanishing of complementary Bell numbers and irrationality of a p-adic series. This generalization leads to a sequence of polynomials. We partially answer the question of existence of an integral zero of those polynomials.
متن کاملDIGRAPH REPRESENTATIONS OF RATIONAL FUNCTIONS OVER THE p-ADIC NUMBERS
In this paper, we construct a digraph structure on padic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on invariant subsets, by means of graph theoretic properties.
متن کاملRational base number systems for p-adic numbers
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 representat...
متن کاملComputable p–adic Numbers
In the present work the notion of the computable (primitive recursive, polynomially time computable) p–adic number is introduced and studied. Basic properties of these numbers and the set of indices representing them are established and it is proved that the above defined fields are p–adically closed. Using the notion of a notation system introduced by Y. Moschovakis an abstract characterizatio...
متن کاملAnalysis Of Exact Solution Of Linear Equation Systems Over Rational Numbers By Parallel p-adic Arithmetic
We study and investigate the p-adic arithmetic along with analysis of exact solution of linear equation systems over rational numbers. Initially we study the basic concepts involving the p-adic numbers and why they form a better representation. After that we describe a parallel implementation of an algorithm for solving systems of linear equations over the field of rational number based on the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2007
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa130-4-8