On small fractional parts of polynomials

2007/11/12 by Nikolay G. Moshchevitin, Moshchevitin, Nikolay G.
Mathematics · #11J54 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11J54

paper · pdf · doi:10.48550/arxiv.0711.1753

8 pages

arxiv created 2007/11/12 · arxiv updated 2009/12/01

Abstract

We prove that for any real polynomial f(x) ∈ℝ [x] the set \α∈ ℝ: \liminf_{n→ ∞} nlog n ||αf(n)|| >0\ has positive Hausdorff dimension. Here ||ξ|| means the distance from ξ to the nearest integer. Our result is based on an original method due to Y. Peres and W. Schlag.

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