The integer transfinite diameter of intervals and totally real algebraic integers

DOI10.5802/jtnb.193zbMath0892.11033OpenAlexW2017853853MaRDI QIDQ1382098

Valerie Flammang, Georges Rhin, Christopher J. Smyth

Publication date: 25 March 1998

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1997__9_1_137_0

zbMATH Keywords

inequalityMahler measuretotally real algebraic integerspolynomialinteger transfinite diametersmall intervalscritical polynomialsFarey intervals

Mathematics Subject Classification ID

Polynomials (irreducibility, etc.) (11R09) Algebraic numbers; rings of algebraic integers (11R04) Totally real fields (11R80)

Related Items (15)

On the linear independence measure of logarithms of rational numbers ⋮ The multivariate integer Chebyshev problem ⋮ Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces ⋮ Algebraic integers whose conjugates all lie in an ellipse ⋮ Applications of Integer Semi-Infinite Programing to the Integer Chebyshev Problem ⋮ The absolute trace of totally positive algebraic integers ⋮ The trace of totally positive algebraic integers ⋮ Generalized Gorshkov–Wirsing Polynomials and the Integer Chebyshev Problem ⋮ A new exceptional polynomial for the integer transfinite diameter of \([0,1\)] ⋮ Monic integer Chebyshev problem ⋮ Integer transfinite diameter and polynomials with small Mahler measure ⋮ Heights of polynomials over lemniscates ⋮ The monic integer transfinite diameter ⋮ On integer Chebyshev polynomials ⋮ Small polynomials with integer coefficients

Cites Work

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• Sur le diamètre transfini entier d'un intervalle réel. (On the transfinite integer diameter of a real interval)
• Totally positive algebraic integers of small trace
• On the asymptotic structure of the polynomials on minimal diophantic deviation from zero
• Sur le diamètre transfini entier d'un intervalle à extrémités rationnelles. (On the integer transfinite diameter of intervals with rational end points.)
• On the length of totally positive algebraic integers
• Rational iteration: complex analytic dynamical systems
• On integer Chebyshev polynomials
• The Mean Values of Totally Real Algebraic Integers
• Comparaison de Deux Mesures de Polynômes
• The integer Chebyshev problem

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