DOI
https://doi.org/10.25772/HERF-BY93
Defense Date
2016
Document Type
Thesis
Degree Name
Master of Science
Department
Mathematical Sciences
First Advisor
Craig Larson
Second Advisor
Sean Cox
Third Advisor
Paul Brooks
Abstract
This paper is a study on some upper bounds of the Mertens function, which is often considered somewhat of a ``mysterious" function in mathematics and is closely related to the Riemann Hypothesis. We discuss some known bounds of the Mertens function, and also seek new bounds with the help of an automated conjecture-making program named CONJECTURING, which was created by C. Larson and N. Van Cleemput, and inspired by Fajtowicz's Dalmatian Heuristic. By utilizing this powerful program, we were able to form, validate, and disprove hypotheses regarding the Mertens function and how it is bounded.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
8-12-2016