Zeros of the Dedekind Zeta-Function

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.

Name thesis:degree_name

M.S. in Mathematics

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2019

Author dc:creator

• Alsharif, Mashael

Contributors dc:contributor

• Micah B. Milinovich

• 3D Printing
• Additive construction
• GnP
• MPC paste
• Mathematics

Repository record dc:identifier

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

OAI identifier oai:identifier

oai:egrove.olemiss.edu:etd-2541