Fourier analysis in Diophantine approximation

Abstract: A real number $x$ is said to be normal if the sequence $a^n x$ is uniformly distributed modulo 1 for every integer $a≥2$. Although Lebesgue-almost all numbers are normal, the problem determining whether specific irrational numbers such as $e$ and $π$ are normal is extremely difficult. However, techniques from Fourier analysis and geometric measure theory can be used to show that certain “thin” subsets of $\mathbb{R}$ must contain normal numbers.

classical analysis and ODEsnumber theory

Audience: researchers in the topic

Topology and Geometry Seminar (Texas, Kansas)