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

Included in

Number Theory Commons

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