Small Polynomials with Integer Coefficients
نویسنده
چکیده
The primary goal of this paper is the study of polynomials with integer coefficients that minimize the sup norm on the set E. In particular, we consider the asymptotic behavior of these polynomials and of their zeros. Let Pn(C) and Pn(Z) be the classes of algebraic polynomials of degree at most n, respectively with complex and with integer coefficients. The problem of minimizing the uniform norm on E by monic polynomials from Pn(C) is well known as the Chebyshev problem (see [4], [31], [43], [16], etc.) In the classical case E = [−1, 1], the explicit solution of this problem is given by the monic Chebyshev polynomial of degree n:
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