Polynomials with Restricted Coefficients and Prescribed Noncyclotomic Factors

DOI10.1112/S1461157000000474zbMath1134.11319MaRDI QIDQ4827618

Michael J. Mossinghoff

Publication date: 18 November 2004

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

Full work available at URL: http://www.lms.ac.uk/jcm/6/lms2003-013/

zbMATH Keywords

Littlewood polynomialsNyman polynomials

Mathematics Subject Classification ID

Polynomials in number theory (11C08) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Polynomials and rational functions of one complex variable (30C10) Analytic computations (11Y35)

Related Items (11)

Double roots of random Littlewood polynomials ⋮ On roots of polynomials with positive coefficients ⋮ Pseudo-Boolean functions and the multiplicity of the zeros of polynomials ⋮ On Littlewood and Newman polynomial multiples of Borwein polynomials ⋮ Negative Pisot and Salem numbers as roots of Newman polynomials ⋮ Binary Constant-Length Substitutions and Mahler Measures of Borwein Polynomials ⋮ On Newman and Littlewood polynomials with a prescribed number of zeros inside the unit disk ⋮ On the Multiplicity of the Zeros of Polynomials with Constrained Coefficients ⋮ On Newman polynomials which divide no Littlewood polynomial ⋮ Roots of polynomials of bounded height ⋮ DIOPHANTINE EQUATIONS FOR POLYNOMIALS WITH RESTRICTED COEFFICIENTS, I (POWER VALUES)

Uses Software

• NTL

Cites Work

• Factoring polynomials with rational coefficients
• On the order of vanishing at 1 of a polynomial
• Factorization of certain cyclotomic functions
• Three problems for polynomials of small measure
• Reciprocal Polynomials Having Small Measure
• Polynomials with small Mahler measure
• Perturbing polynomials with all their roots on the unit circle
• On a problem of Byrnes concerning polynomials with restricted coefficients
• Littlewood-Type Problems on [0,1]
• Polynomials with Height 1 and Prescribed Vanishing at 1
• On a problem of Byrnes concerning polynomials with restricted coefficients, II
• Multiple Roots of [−1, 1 Power Series]
• Newman polynomials with prescribed vanishing and integer sets with distinct subset sums
• Exceptional Units and Numbers of Small Mahler Measure
• On the Product of the Conjugates outside the unit circle of an Algebraic Integer

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