Keywords

Riemann zeta function, hurwtiz zeta function, l functions, dedekind zeta function, universality, prime number theorem, riemann hypothesis, generalized riemann hypothesis, analytic number theory, special functions

Abstract

In this thesis we provide a body of knowledge that concerns Riemann zeta-function and its generalizations in a cohesive manner. In particular, we have studied and mentioned some recent results regarding Hurwitz and Lerch functions, as well as Dirichlet's L-function. We have also investigated some fundamental concepts related to these functions and their universality properties. In addition, we also discuss different formulations and approaches to the proof of the Prime Number Theorem and the Riemann Hypothesis. These two topics constitute the main theme of this thesis. For the Prime Number Theorem, we provide a thorough discussion that compares and contrasts Norbert Wiener's proof with that of Newman's short proof. We have also related them to Hadamard's and de la Vallee Poussin's original proofs written in 1896. As far as the Riemann Hypothesis is concerned, we discuss some recent results related to equivalent formulations of the Riemann Hypothesis as well as the Generalized Riemann Hypothesis.

Notes

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Graduation Date

2015

Semester

Spring

Advisor

Mohapatra, Ram N.

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science

Format

application/pdf

Identifier

CFE0005576

URL

http://purl.fcla.edu/fcla/etd/CFE0005576

Language

English

Release Date

May 2015

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

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Included in

Mathematics Commons

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