Rational numbers near self-similar sets

Han Yu (University of Cambridge)

12-Apr-2021, 16:15-17:30 (3 years ago)

Abstract: We will discuss a problem on counting rational numbers near self-similar sets. In particular, we will show that the set of rational numbers is ‘reasonably well distributed’ around the middle $p$-th Cantor set when $p$ is a large integer. Our approach is via Fourier analysis and we will also discuss some problems on Fourier transform of self-similar measures which are of independent interest. As a result, it is possible to show that $p=5$ satisfies the previous statement. The materials come from various working-in-progress projects with D. Allen, S. Chow and P. Varju.

dynamical systemsnumber theory

Audience: general audience


New England Dynamics and Number Theory Seminar

Organizers: Dmitry Kleinbock, Han Li*, Lam Pham, Felipe Ramirez
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