{"id":{"repo_id":"siu-theses","oai_identifier":"oai:opensiuc.lib.siu.edu:dissertations-2030"},"canonical_url":"https://search.dev.ndltd.org/etd/siu-theses/oai:opensiuc.lib.siu.edu:dissertations-2030","repository":{"repo_id":"siu-theses","name":"Southern Illinois University","base_url":"https://opensiuc.lib.siu.edu/do/oai/"},"display":{"title":"Determination of Quadratic Lattices by Local Structure and Sublattices of Codimension One","abstract":"For definite quadratic lattices over the rings of integers of algebraic number fields, it is shown that lattices are determined up to isometry by their local structure and sublattices of codimension 1. In particular, a theorem of Yoshiyuki Kitaoka for $\\mathbb{Z}$-lattices is generalized to definite lattices over algebraic number fields.","abstract_html":"For definite quadratic lattices over the rings of integers of algebraic number fields, it is shown that lattices are determined up to isometry by their local structure and sublattices of codimension 1. In particular, a theorem of Yoshiyuki Kitaoka for $\\mathbb{Z}$-lattices is generalized to definite lattices over algebraic number fields.","abstract_has_math":true,"creators":["Meyer, Nicolas David"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Campus Only Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Earnest, Andrew","Pericak-Spector, Kathleen"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-05-01T07:00:00Z","date_published":"2015-05-01T07:00:00Z","updated_at":"2026-07-24T04:34:36Z","subjects":["Algebraic Number Theory","Quadratic Forms"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opensiuc.lib.siu.edu/dissertations/1026","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Earnest, Andrew","Pericak-Spector, Kathleen"]},{"key":"dc:creator","label":"Author","values":["Meyer, Nicolas David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Only Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic Number Theory","Quadratic Forms"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://opensiuc.lib.siu.edu/dissertations/1026"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["For definite quadratic lattices over the rings of integers of algebraic number fields, it is shown that lattices are determined up to isometry by their local structure and sublattices of codimension 1. In particular, a theorem of Yoshiyuki Kitaoka for $\\mathbb{Z}$-lattices is generalized to definite lattices over algebraic number fields."]},{"key":"dc:title","label":"Title","values":["Determination of Quadratic Lattices by Local Structure and Sublattices of Codimension One"]}]}],"canonical_facts":{"dc:contributor":["Earnest, Andrew","Pericak-Spector, Kathleen"],"dc:creator":["Meyer, Nicolas David"],"dc:description.abstract":["For definite quadratic lattices over the rings of integers of algebraic number fields, it is shown that lattices are determined up to isometry by their local structure and sublattices of codimension 1. In particular, a theorem of Yoshiyuki Kitaoka for $\\mathbb{Z}$-lattices is generalized to definite lattices over algebraic number fields."],"dc:identifier":["https://opensiuc.lib.siu.edu/dissertations/1026"],"dc:subject":["Algebraic Number Theory","Quadratic Forms"],"dc:title":["Determination of Quadratic Lattices by Local Structure and Sublattices of Codimension One"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Campus Only Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T04:34:36Z"}