@Article{Lipnicki2016,
author = "Lipnicki, Artur",
title = "Uniform approximation by polynomials with integer coefficients",
journal = "Opuscula Math.",
year = "2016",
volume = "36",
number = "4",
pages = "489--498",
doi = "http://dx.doi.org/10.7494/OpMath.2016.36.4.489",
url = "http://dx.doi.org/10.7494/OpMath.2016.36.4.489",
abstract = "Let \(r\), \(n\) be positive integers with \(n\ge 6r\). Let \(P\) be a polynomial of degree at most \(n\) on \([0,1]\) with real coefficients, such that \(P^{(k)}(0)/k!\) and \(P^{(k)}(1)/k!\) are integers for \(k=0,\dots,r-1\). It is proved that there is a polynomial \(Q\) of degree at most \(n\) with integer coefficients such that \(|P(x)-Q(x)|\le C_1C_2^r r^{2r+1/2}n^{-2r}\) for \(x\in[0,1]\), where \(C_1\), \(C_2\) are some numerical constants. The result is the best possible up to the constants.",
keywords = "approximation by polynomials with integer coefficients, lattice, covering radius",
issn = "1232-9274"
}