On small fractional parts of polynomials
Abstract
Description
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.
8 pages
8 pages