{"id":{"repo_id":"mississippi","oai_identifier":"oai:egrove.olemiss.edu:etd-2541"},"canonical_url":"https://search.dev.ndltd.org/etd/mississippi/oai:egrove.olemiss.edu:etd-2541","repository":{"repo_id":"mississippi","name":"University of Mississippi","base_url":"https://egrove.olemiss.edu/do/oai/"},"display":{"title":"Zeros of the Dedekind Zeta-Function","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Alsharif, Mashael"],"institution":null,"degree_name":"M.S. in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Micah B. Milinovich"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-01-01T08:00:00Z","date_published":"2019-01-01T08:00:00Z","updated_at":"2026-07-24T03:07:00Z","subjects":["3D Printing","Additive construction","GnP","MPC paste","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://egrove.olemiss.edu/etd/1542","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Micah B. Milinovich"]},{"key":"dc:creator","label":"Author","values":["Alsharif, Mashael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2020-01-23T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S. in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["3D Printing","Additive construction","GnP","MPC paste","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://egrove.olemiss.edu/etd/1542"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Zeros of the Dedekind Zeta-Function"]}]}],"canonical_facts":{"dc:contributor":["Micah B. Milinovich"],"dc:creator":["Alsharif, Mashael"],"dc:date.available":["2020-01-23T08:00:00Z"],"dc:description.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."],"dc:identifier":["https://egrove.olemiss.edu/etd/1542"],"dc:subject":["3D Printing","Additive construction","GnP","MPC paste","Mathematics"],"dc:title":["Zeros of the Dedekind Zeta-Function"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S. in Mathematics"]},"updated_at":"2026-07-24T03:07:00Z"}