On beta expansions for Pisot numbers

DOI10.1090/S0025-5718-96-00693-XzbMath0855.11039OpenAlexW2052550900MaRDI QIDQ4878586

David W. Boyd

Publication date: 30 January 1997

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-96-00693-x

zbMATH Keywords

polynomialsPisot numbersbeta expansionsbeta-number

Mathematics Subject Classification ID

Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Computational number theory (11Y99)

Related Items (11)

On gaps in Rényi \(\beta\)-expansions of unity for \(\beta>1\) an algebraic number ⋮ Number of digit changes in \(\beta\)-expansion of unity in \(\mathbb{F}_q((x^{-1}))\) ⋮ \(\beta\)-expansion and transcendence in \(\mathbb F_q((x^{-1}))\) ⋮ Linear recurrent cryptography: Golden-like cryptography for higher order linear recurrences ⋮ On the distribution of certain Pisot numbers ⋮ BETA ENCODERS: SYMBOLIC DYNAMICS AND ELECTRONIC IMPLEMENTATION ⋮ Some computations on the spectra of Pisot and Salem numbers ⋮ On the dichotomy of Perron numbers and beta-conjugates ⋮ Asymptotic behavior of beta-integers ⋮ SUR LE BÊTA-DÉVELOPPEMENT DE 1 DANS LE CORPS DES SÉRIES FORMELLES ⋮ On univoque Pisot numbers

Uses Software

• Maple

Cites Work

• A problem of Boyd concerning geometric means of polynomials
• Pisot numbers in the neighbourhood of a limit point. I
• Small Salem numbers
• A remarkable class of algebraic integers. Proof of a conjecture of Vijayaraghavan
• Finite beta-expansions
• On theβ-expansions of real numbers
• Développement en base $\theta$, répartition modulo un de la suite $(x\theta \sp n)$, n$\ge 0$, langages codés et $\theta$-shift
• Reciprocal Polynomials Having Small Measure
• Speculations Concerning the Range of Mahler's Measure
• On Periodic Expansions of Pisot Numbers and Salem Numbers
• Pisot and Salem Numbers in Intervals of the Real Line
• Conjugates of Beta-Numbers and the Zero-Free Domain for a Class of Analytic Functions
• Computability by finite automata and pisot bases
• The zeta function of the beta transformation
• Ensembles fermés de nombres algébriques
• Étude de certaines fonctions méromorphes bornées sur le cercle unité. Application à un ensemble fermé d'entiers algébriques
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