{"id":{"repo_id":"unm","oai_identifier":"oai:digitalrepository.unm.edu:math_etds-1018"},"canonical_url":"https://search.dev.ndltd.org/etd/unm/oai:digitalrepository.unm.edu:math_etds-1018","repository":{"repo_id":"unm","name":"University of New Mexico","base_url":"https://digitalrepository.unm.edu/do/oai/"},"display":{"title":"Arithmetic Differential Subgroups of GL_{n}","abstract":"A remarkable and special Galois Theory appears from the study of the arithmetic analogue of ordinary differential equations; where functions are replaced by integers, the derivative operator replaced by the Fermat quotient operator' and differential equations are replaced by arithmetic differential equations. The main result presented in the thesis will be the study of a very special class of arithmetic subgroups of GL_n. We also introduce a set of functions, that we call Leibniz systems. These functions 'generate' some examples of the differential subgroups of GL_n. As a by-product we found more analogies between the ordinary differential operator and the Fermat quotient operator, such as the chain rule and the product rule.","abstract_html":"A remarkable and special Galois Theory appears from the study of the arithmetic analogue of ordinary differential equations; where functions are replaced by integers, the derivative operator replaced by the Fermat quotient operator' and differential equations are replaced by arithmetic differential equations. The main result presented in the thesis will be the study of a very special class of arithmetic subgroups of GL_n. We also introduce a set of functions, that we call Leibniz systems. These functions 'generate' some examples of the differential subgroups of GL_n. As a by-product we found more analogies between the ordinary differential operator and the Fermat quotient operator, such as the chain rule and the product rule.","abstract_has_math":false,"creators":["Heras-Llanos, Alfonso E"],"institution":null,"degree_name":"Mathematics","degree_level":"Doctoral","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Buium, Alexandr","Alexandru Buium","Charles Boyer","Janet Vassilev","Lance Miller"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-07-12T07:00:00Z","date_published":"2014-07-12T07:00:00Z","updated_at":"2026-07-24T05:27:37Z","subjects":["Arihmetic differential Subgroups og GL_{n}"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalrepository.unm.edu/math_etds/19"],"render_values":[{"text":"https://digitalrepository.unm.edu/math_etds/19","href":"https://digitalrepository.unm.edu/math_etds/19","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1928/24316","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Buium, Alexandr","Alexandru Buium","Charles Boyer","Janet Vassilev","Lance Miller"]},{"key":"dc:creator","label":"Author","values":["Heras-Llanos, Alfonso E"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral","Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Arihmetic differential Subgroups og GL_{n}"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/1928/24316","https://digitalrepository.unm.edu/math_etds/19"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A remarkable and special Galois Theory appears from the study of the arithmetic analogue of ordinary differential equations; where functions are replaced by integers, the derivative operator replaced by the Fermat quotient operator' and differential equations are replaced by arithmetic differential equations. The main result presented in the thesis will be the study of a very special class of arithmetic subgroups of GL_n. We also introduce a set of functions, that we call Leibniz systems. These functions 'generate' some examples of the differential subgroups of GL_n. As a by-product we found more analogies between the ordinary differential operator and the Fermat quotient operator, such as the chain rule and the product rule."]},{"key":"dc:title","label":"Title","values":["Arithmetic Differential Subgroups of GL_{n}"]}]}],"canonical_facts":{"dc:contributor":["Buium, Alexandr","Alexandru Buium","Charles Boyer","Janet Vassilev","Lance Miller"],"dc:creator":["Heras-Llanos, Alfonso E"],"dc:description.abstract":["A remarkable and special Galois Theory appears from the study of the arithmetic analogue of ordinary differential equations; where functions are replaced by integers, the derivative operator replaced by the Fermat quotient operator' and differential equations are replaced by arithmetic differential equations. The main result presented in the thesis will be the study of a very special class of arithmetic subgroups of GL_n. We also introduce a set of functions, that we call Leibniz systems. These functions 'generate' some examples of the differential subgroups of GL_n. As a by-product we found more analogies between the ordinary differential operator and the Fermat quotient operator, such as the chain rule and the product rule."],"dc:identifier":["http://hdl.handle.net/1928/24316","https://digitalrepository.unm.edu/math_etds/19"],"dc:language":["English"],"dc:subject":["Arihmetic differential Subgroups og GL_{n}"],"dc:title":["Arithmetic Differential Subgroups of GL_{n}"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Doctoral","Dissertation"],"thesis:degree_name":["Mathematics"]},"updated_at":"2026-07-24T05:27:37Z"}