There are infinitely many limit points of the fractional parts of powers |
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| Authors: | Artūras Dubickas |
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| Affiliation: | (1) Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania |
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| Abstract: | Suppose that α > 1 is an algebraic number and ξ > 0 is a real number. We prove that the sequence of fractional partsξα
n
, n = 1, 2, 3, …, has infinitely many limit points except when α is a PV-number and ξ ∈ ℚ(α). For ξ = 1 and α being a rational
non-integer number, this result was proved by Vijayaraghavan. |
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| Keywords: | Limit points fractional parts PV-numbers Salem numbers |
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