Bulletin of the Belgian Mathematical Society - Simon Stevin

Arithmetics on beta-expansions with Pisot bases over $F_q((x^{-1}))$

R. Ghorbel, M. Hbaib, and S. Zouari

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Abstract

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 $L_\odot$. 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 $L_\odot$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 2 (2014), 241-251.

Dates
First available in Project Euclid: 20 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1400592622

Digital Object Identifier
doi:10.36045/bbms/1400592622

Mathematical Reviews number (MathSciNet)
MR3211013

Zentralblatt MATH identifier
1376.11070

Subjects
Primary: 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure 37B50: Multi-dimensional shifts of finite type, tiling dynamics

Keywords
Formal power series $\beta$-expansion quadratic Pisot unit

Citation

Ghorbel, R.; Hbaib, M.; Zouari, S. Arithmetics on beta-expansions with Pisot bases over $F_q((x^{-1}))$. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 2, 241--251. doi:10.36045/bbms/1400592622. https://projecteuclid.org/euclid.bbms/1400592622


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