# Elan Segarra

Harvey Mudd College Mathematics 2005-2006

Thesis Proposal: | An Exploration of the Riemann Zeta Function |
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Thesis Advisors: | Prof. Darryl Yong and Michael Raugh |

Second Reader: | Prof. Lesley Ward |

E-Mail: | esegarra@hmc.edu |

Thesis: | An Exploration of the Riemann Zeta Function and its Application to Prime Number Distribution |

## An Exploration of the Riemann Zeta-Function and its Application to the Theory of Prime Number Distribution

Identified as one of the 7 Millennium Problems, the Riemann zeta hypothesis has successfully evaded mathematicians for over 100 years. Simply stated, Riemann conjectured that all of the nontrivial zeroes of his zeta function have real part equal to 1/2. This thesis attempts to explore the theory behind Riemann's zeta function by first starting with Euler's zeta series and building up to Riemann's function. Along the way we will develop the math required to handle this theory in hopes that by the end the reader will have immersed themselves enough to pursue their own exploration and research into this fascinating subject.