Polynomials with integer coefficients and their zeros

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 the approximation by polynomials with integer coefficients, and to the growth of...

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Bibliographic Details
Published in:	Journal of mathematical sciences (New York, N.Y.) Vol. 183; no. 6; pp. 810 - 822
Main Author:	Pritsker, Igor E.
Format:	Journal Article
Language:	English
Published:	Boston Springer US 11.06.2012 Springer
Subjects:	Mathematics Mathematics and Statistics distribution of zeros algebraic numbers Polynomials
ISSN:	1072-3374, 1573-8795
Online Access:	Get full text
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Summary:	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 the 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.
ISSN:	1072-3374 1573-8795
DOI:	10.1007/s10958-012-0842-z