On small fractional parts of polynomials

Nikolay G. Moshchevitin

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arXiv · 0711.1753

On small fractional parts of polynomials

Nikolay G. Moshchevitin

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Abstract

We prove that for any real polynomial $f(x) \in\mathbb{R} [x]$ the set $$ \{α\in \mathbb{R}: \liminf_{n\to \infty} n\log n ||αf(n)|| >0\} $$ 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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Nikolay G. Moshchevitin. 2007-11-12. On small fractional parts of polynomials. https://arxiv.org/abs/0711.1753

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