Electronic Theses and Dissertations

Date of Award

2019

Document Type

Thesis

Degree Name

M.S. in Mathematics

Department

Mathematics

First Advisor

Micah Milinovich

Relational Format

dissertation/thesis

Abstract

H. L. Montgomery proved a formula for sums over two sets of nontrivial zeros of the Riemann zeta-function. Assuming the Riemann Hypothesis, he used this formula and Fourier analysis to prove an estimate for the proportion of simple zeros of the Riemann zeta-function. We prove a generalization of his formula for the nontrivial zeros of the Dedekind zeta-function of a Galois number field, and use this formula and Fourier analysis to prove an estimate for the proportion of distinct zeros, assuming the Generalized Riemann Hypothesis.

Included in

Mathematics Commons

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