On the beta expansion for Salem numbers of degree 6

DOI10.1090/S0025-5718-96-00700-4zbMath0848.11048OpenAlexW2093561257MaRDI QIDQ4878587

David W. Boyd

Publication date: 14 May 1996

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-96-00700-4

zbMATH Keywords

beta expansionsbeta numberSchmidt's conjectureSalem numbers of degree 6

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

Dynamical directions in numeration ⋮ On gaps in Rényi \(\beta\)-expansions of unity for \(\beta>1\) an algebraic number ⋮ Periodicity ofβ-expansions for certain Pisot units ⋮ On Salem half-norms ⋮ Beta expansion for some particular sequences of Salem numbers ⋮ On periodic representations in non-Pisot bases ⋮ On periodic alternate base expansions ⋮ A note on non-periodic greedy expansions in Salem base ⋮ Periodic expansion of one by Salem numbers ⋮ The beta-transformation's companion map for Pisot or Salem numbers and their periodic orbits ⋮ Beta-expansions for infinite families of Pisot and Salem numbers ⋮ Automatic \(\beta\)-expansions of formal Laurent series over finite fields ⋮ On the beta expansion of Salem numbers of degree 8 ⋮ Dynamics forβ-shifts and Diophantine approximation ⋮ Finiteness and periodicity of beta expansions – number theoretical and dynamical open problems ⋮ Periodic representations in Salem bases ⋮ Beta-expansions of -adic numbers ⋮ A family of non-sofic beta expansions ⋮ Compact quotients of Cahen-Wallach spaces ⋮ On the dichotomy of Perron numbers and beta-conjugates ⋮ On the co-factors of degree 6 Salem number beta expansions ⋮ On the zeros of the derivatives of certain polynomials ⋮ Seventy years of Salem numbers ⋮ On relations for rings generated by algebraic numbers and their conjugates ⋮ On univoque Pisot numbers ⋮ On the beta-expansions of 1 and algebraic numbers for a Salem number beta ⋮ Symbolic representations of nonexpansive group automorphisms

Cites Work

• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• On Periodic Expansions of Pisot Numbers and Salem Numbers
• Conjugates of Beta-Numbers and the Zero-Free Domain for a Class of Analytic Functions
• The zeta function of the beta transformation
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