turkmath.org

This talk aims to explain the recent solution of a problem in metric number theory, originating from Diophantine approximations. We will be concerned with the existence of explicitly defined infinite families of sequences of real numbers in [0,1), exhibiting particular distribution properties. We will first give a brief introduction to sequences that are “uniformly distributed mod. 1”. We will then describe the problem, and the tools to solve it. Our methods are based on the work on permutation polynomials over finite fields, due to the speaker and her collaborators, and on low discrepancy sequences, obtained by Pausinger. A recent result of Bourgain and Kontorovich on Zaremba’s Conjecture enables us to solve the existence problem completely. No prior knowledge of uniform distribution theory will be assumed. This is joint work with Florian Pausinger.