### A problem of Hausdorff measure and approximation by polynomials

Linfoot Number Theory Seminar

3rd April 2019, 11:00 am – 12:00 pm

Howard House, 4th Floor Seminar Room

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 $n > 3$.

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