journal article
oaidoi:10.1016/j.jnt.2008.07.008

On small fractional parts of polynomials

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Publication date
28 February 2009
Publisher
Elsevier Inc.
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    Abstract

    AbstractTextWe prove that for any real polynomial f(x)∈R[x] the set{α∈R:lim infn→∞nlogn‖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.VideoFor a video summary of this paper, please visit http://www.youtube.com/watch?v=GNWDrfQnV2c

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