Some computations on the spectra of Pisot and Salem numbers

DOI10.1090/S0025-5718-01-01336-9zbMath1037.11065MaRDI QIDQ2781224

Kevin G. Hare, Peter B. Borwein

Publication date: 19 March 2002

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

zbMATH Keywords

spectrumPisot numbersLLL algorithm

Mathematics Subject Classification ID

PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Evaluation of number-theoretic constants (11Y60)

Related Items (18)

Bernoulli convolutions associated with certain non-Pisot numbers ⋮ Spectral properties of cubic complex Pisot units ⋮ On the topology of polynomials with bounded integer coefficients ⋮ On spectra of neither Pisot nor Salem algebraic integers ⋮ Discrete spectra and Pisot numbers ⋮ The Reciprocal Algebraic Integers Having Small House ⋮ On Littlewood and Newman polynomial multiples of Borwein polynomials ⋮ A proof of the Erdős-Joó-Komornik conjecture in the case of formal power series ⋮ The structure of the spectra of Pisot numbers. ⋮ Approximation by polynomials with bounded coefficients ⋮ On certain multiples of Littlewood and Newman polynomials ⋮ On an approximation property of Pisot numbers. II ⋮ A property of the spectra of non-Pisot numbers ⋮ Non-trivial quadratic approximations to zero of a family of cubic Pisot numbers ⋮ A remark on the spectra of Pisot numbers ⋮ Unique expansions of real numbers ⋮ Approximation by polynomials with coefficients \(\pm 1\). ⋮ Seventy years of Salem numbers

Cites Work

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• Factoring polynomials with rational coefficients
• Developments in non-integer bases
• On a property of Pisot numbers and related questions
• Dimension of a family of singular Bernoulli convolutions
• Approximation by polynomials with coefficients \(\pm 1\).
• An approximation property of Pisot numbers
• Power series with integral coefficients
• Arithmetic Properties of Bernoulli Convolutions
• Pisot and Salem Numbers in Intervals of the Real Line
• On the sequence of numbers of the form $ε₀ + ε₁q + ... + ε_nq^n$, $ε_i ∈ {0,1}$
• On a problem of Tamas Varga
• On beta expansions for Pisot numbers
• Characterization of the unique expansions $1=\sum^{\infty}_{i=1}q^{-n_ i}$ and related problems

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