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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Vydáno v:Journal of mathematical sciences (New York, N.Y.) Ročník 183; číslo 6; s. 810 - 822
Hlavní autor: Pritsker, Igor E.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 11.06.2012
Springer
Témata:
Mathematics
Mathematics and Statistics
distribution of zeros
algebraic numbers
Polynomials
ISSN:1072-3374, 1573-8795
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Shrnutí: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