Polynomials with integer coefficients and their zeros

Igor E. Pritsker

Polynomials with integer coefficients and their zeros

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arxiv 1307.6200 v1 pith:A2FGXBEA submitted 2013-07-23 math.NT

Igor E. Pritsker This is my paper · ORCID

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keywords coefficientsintegerpolynomialsproblemszerosalgebraicapplicationsapproximation

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We study several related problems on polynomials with integer coefficients. This includes the integer Chebyshev problem, and the Schur problems on means of algebraic numbers. We also discuss interesting applications to approximation by polynomials with integer coefficients, and to the growth of coefficients for polynomials with roots located in prescribed sets. The distribution of zeros for polynomials with integer coefficients plays an important role in all of these problems.

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math.CA 2024-12 conditional novelty 5.0 of 10

For a family of nonlinear recurrences, the paper evaluates the asymptotic constant C to 25 digits using a reciprocal transformation and the Mavecha-Laohakosol algorithm.

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