Date of Award

Spring 2024

Abstract

We prove an entropic version of van der Corput’s difference theorem: the entropy of a sequence is equal to the entropy of its differences. This reveals a correspondence between the theory of uniform distribution mod 1 and entropy. As applications, we establish several entropic versions of other uniform distribution theorems.

Document Type

Dissertation

First Advisor

Liming Ge

Second Advisor

Maria Basterra

Third Advisor

Rita A. Hibschweiler

Department or Program

Mathematics

Degree Name

Doctor of Philosophy

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