#### Date of Award

2019

#### Document Type

Thesis

#### Degree Name

M.S. in Mathematics

#### Department

Mathematics

#### First Advisor

Micah B. 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.

#### Recommended Citation

Alsharif, Mashael, "Zeros of the Dedekind Zeta-Function" (2019). *Electronic Theses and Dissertations*. 1542.

https://egrove.olemiss.edu/etd/1542