A PROOF OF THE RIEMANN HYPOTHESIS

A Dissertation

Submitted to the Graduate Faculty of the

Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy

in

The Department of Mathematics

by Steven S. Smart B.S. in Math., Elite University, 19XX M.S., Louisiana State University, 19XX May 20XX

Acknowledgments

This dissertation would not be possible without several contributions. It is a pleasure to thank ...............

This work was motivated by Example 4.3.14 in [1] brought to my attention by ...............

It is a pleasure also to thank .............. for providing me with a pleasant working environment. A special thanks to Dr. X. Y. Z for

This dissertation is dedicated to ................ for their support an encouragement.

Table of Contents

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. First Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2. Second Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3. Third Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4. Fourth Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5. Fifth Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Vita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

List of Figures

1 Forming a Hexagonal Linkage from Two Free Linkages . . . . . . . 2

Abstract

In this work ....................... we begin with a brief survey of ................... We accomplish this in the following two chapters.

.................... These properties are used in Chapter 5.

Introduction

1

1. First Step

Consider the following figure.

FIGURE 1. Forming a Hexagonal Linkage from Two Free Linkages

2. Second Step

3

3. Third Step

4

4. Fourth Step

5

5. Fifth Step

6

References

[1] G. Glibb and S. Slick, Propositions equivalent to the Riemann Hypothesis, Brooklyn Bridge studies in advanced mathematics, 18, Brooklyn Bridge University Press, 1999.

Vita

Steven S. Smart was born on October xx 19xx, in YY City, Ohio. He finished his undergraduate studies at Elite University May 19XX. He earned a master of science degree in mathematics from Louisiana State University in May 19YY. In August 19ZZ he came to Louisiana State University to pursue graduate studies in mathematics. He is currently a candidate for the degree of Doctor of Philosophy in mathematics, which will be awarded in August 20XX.