Arithmetics on beta-expansions with Pisot bases over [F.sub.q]

In this paper we consider finite [beta]-expansions in the field of formal series with Pisot basis [beta]. We are studying the arithmetic operations on [beta]-expansions and provide bounds on the number of fractional digits arising in multiplication for arbitrary [beta]-polynomials noted [L.sub.[??]]...

Full description

Saved in:
Bibliographic Details
Published in:Bulletin of the Belgian Mathematical Society, Simon Stevin Simon Stevin, 2014-04, Vol.21 (2), p.241
Main Authors: Ghorbel, R, Hbaib, M, Zouari, S
Format: Article
Language:English
Subjects:
Analysis
Arithmetic
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we consider finite [beta]-expansions in the field of formal series with Pisot basis [beta]. We are studying the arithmetic operations on [beta]-expansions and provide bounds on the number of fractional digits arising in multiplication for arbitrary [beta]-polynomials noted [L.sub.[??]]. This value is given explicitly for families of Pisot basis. The last part of this paper is devoted to quadratic Pisot series where we will give the exact value for [L.sub.[??]]. Key words and phrases : Formal power series, [beta]-expansion, quadratic Pisot unit.
ISSN:1370-1444
2034-1970