Alessandro Pezzoni

A problem of Hausdorff measure and approximation by polynomials

The study of the set $L_n(w)$ of points $x \in \mathbb{R}$ for which there are
infinitely many integer polynomials of degree up to $n$ such that
| P(x) |< H(P)^{-w} has a long history, which dates back to 1932 with Kurt Mahler. In this talk we will introduce this problem in the context of Metric Number Theory and we shall show how to determine the Hausdorff measure of $L_3(w)$. Time permitting, we will also discuss how one might try to do this for $n > 3$.