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Arithmetical properties of linear recurrent sequences

✍ Scribed by Artūras Dubickas

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
140 KB
Volume
122
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let F (z) ∈ R[z] be a polynomial with positive leading coefficient, and let α > 1 be an algebraic number. For r = deg F > 0, assuming that at least one coefficient of F lies outside the field Q(α) if α is a Pisot number, we prove that the difference between the largest and the smallest limit points of the sequence of fractional parts {F (n)α n } n=1,2,3,... is at least 1/ (P r+1 ), where stands for the so-called reduced length of a polynomial.

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