Chebyshev Polynomials with Integer Coefficients
نویسنده
چکیده
We study the asymptotic structure of polynomials with integer coef cients and smallest uniform norms on an interval of the real line Introducing methods of the weighted potential theory into this problem we improve the bounds for the multiplicities of some factors of the integer Chebyshev polynomials Introduction Let Pn C and Pn Z be the sets of algebraic polynomials of degree at most n respectively with complex and with integer coe cients De ne the uniform norm on the interval a b R by kfk a b max x a b jf x j It is very well known that the Chebyshev polynomial Tn x n cos n arccos x is a monic polynomial of degree n which minimizes the uniform norm on in the class of all monic polynomials from Pn C see and AMS Subject Classi cation Primary C C Secondary A A
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