Speaker: Manos Zafeiropoulos (TU Graz)
10 February, 2021 14:30 UTC
Abstract: Let $\mu$ be a probability measure with $\widehat{\mu}(t)\ll (\log |t|)^{-A}$ for some $A>0$, supported on a set $F\subseteq [0,1]$. Let $\mathcal{A}=(q_n)$ be an increasing sequence of integers. We establish a quantitative inhomogeneous Khintchine-type theorem in which the points of interest lie in $F$ and the “denominators” of the approximants belong to $\mathcal{A}$ in the following cases: (i) $(q_n)$ is lacunary and $A>2$. (ii)The prime divisors of $(q_n)_{n=1}^{\infty}$ are restricted in a set of $k$ prime numbers and $A>2k$.