Approximation by polynomials with bounded coefficients |
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Authors: | Toufik Zaimi |
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Institution: | Département de mathématiques, Centre universitaire Larbi Ben M'hidi, Oum El-Bouaghi 04000, Algérie |
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Abstract: | Let θ be a real number satisfying 1<θ<2, and let A(θ) be the set of polynomials with coefficients in {0,1}, evaluated at θ. Using a result of Bugeaud, we prove by elementary methods that θ is a Pisot number when the set (A(θ)−A(θ)−A(θ)) is discrete; the problem whether Pisot numbers are the only numbers θ such that 0 is not a limit point of (A(θ)−A(θ)) is still unsolved. We also determine the three greatest limit points of the quantities , where C(θ) is the set of polynomials with coefficients in {−1,1}, evaluated at θ, and we find in particular infinitely many Perron numbers θ such that the sets C(θ) are discrete. |
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Keywords: | 11R06 11Y60 11C08 |
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