Video library: N. G. Moshchevitin, On the distribution of (non)primitive lattice points

VIDEO LIBRARY


Memorial Conference on Analytic Number Theory and Applications Dedicated to the 130th Anniversary of I. M. Vinogradov September 14, 2021 17:15, Moscow, Steklov Mathematical Institute, 8, Gubkina str, room 110 + online

On the distribution of (non)primitive lattice points N. G. Moshchevitin Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract: In 1959, Chalk and Erdös proved the following result on coprime inhomogeneous approximation to a real number: for any given $\alpha\in \mathbb{R}\setminus\mathbb{Q}$ and any real number $\eta$, there exists an absolute constant $ \lambda$ such that $$ q\,\|q\alpha - \eta - r\| \leqslant \lambda\left(\frac{\log q}{\log\log q}\right)^2 $$ is satisfied by infinitely many pairs of coprime integers $q$, $r$ with $q\geqslant 1$. In our lecture we discuss some recent related results and generalizations. In particular, we improve on a recent result by Svetlana Jitomirskaya and Wencai Liu.