Reciprocal Polynomials Having Small Measure

DOI10.2307/2006402zbMath0447.12002OpenAlexW4232488423MaRDI QIDQ3892329

David W. Boyd

Publication date: 1980

Full work available at URL: https://doi.org/10.2307/2006402

zbMATH Keywords

Schur convexityGraeffe's methodLehmer's problemmeasure of polynomialssmall measure

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Polynomials (irreducibility, etc.) (11R09) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Software, source code, etc. for problems pertaining to field theory (12-04)

Related Items (28)

Sharp lower bounds for regulators of small-degree number fields ⋮ Algebraic integers whose conjugates all lie in an ellipse ⋮ Polynomials with Restricted Coefficients and Prescribed Noncyclotomic Factors ⋮ On the relations between the zeros of a polynomial and its Mahler measure ⋮ The maximal conjugate of a non-reciprocal algebraic integer ⋮ Lehmer's problem and splitting of rational primes in number fields ⋮ Analytic formulas for the regulator of a number field ⋮ On beta expansions for Pisot numbers ⋮ The arithmetic and geometry of Salem numbers ⋮ Negative Pisot and Salem numbers as roots of Newman polynomials ⋮ Binary Constant-Length Substitutions and Mahler Measures of Borwein Polynomials ⋮ Beta-expansions for infinite families of Pisot and Salem numbers ⋮ On the smallest houses of reciprocal algebraic integers ⋮ On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus ⋮ Lehmer's Question, Knots and Surface Dynamics ⋮ Mahler's measure for polynomials in several variables ⋮ On the Absolute Mahler Measure of Polynomials Having All Zeros in a Sector ⋮ Lehmer's question, graph complexity growth and links ⋮ Integer transfinite diameter and polynomials with small Mahler measure ⋮ The values of Mahler measures ⋮ On the distribution of roots of polynomials in sectors. I ⋮ Reciprocal polynomials having small measure. II ⋮ Polynomials with small Mahler measure ⋮ Perturbing polynomials with all their roots on the unit circle ⋮ The number of unimodular roots of some reciprocal polynomials ⋮ Primes in Sequences Associated to Polynomials (After Lehmer) ⋮ Universal systole bounds for arithmetic locally symmetric spaces ⋮ On the spectrum of the Zhang-Zagier height

Cites Work

• Unnamed Item
• Lectures on transcendental numbers. Edited and completed by B. Diviš and W. J. LeVeque
• Small Salem numbers
• Factorization of certain cyclotomic functions
• On a question of Lehmer and the number of irreducible factors of a polynomial
• Resultant Procedure and the Mechanization of the Graeffe Process
• Variations on a Theme of Kronecker
• Some Inequalities for Polynomials
• Analytic Inequalities
• On the Product of the Conjugates outside the unit circle of an Algebraic Integer

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