{"id":{"repo_id":"unm","oai_identifier":"oai:digitalrepository.unm.edu:math_etds-1048"},"canonical_url":"https://search.dev.ndltd.org/etd/unm/oai:digitalrepository.unm.edu:math_etds-1048","repository":{"repo_id":"unm","name":"University of New Mexico","base_url":"https://digitalrepository.unm.edu/do/oai/"},"display":{"title":"ABC Theorems In The Functional Case","abstract":"In this dissertation we will prove some ABC Theorems, namely for relatively prime by pairs p-adic entire functions in one variable, for p-adic meromorphic functions in several variables without common factors, under the hypothesis that no subsum vanishes, and also for pairwise relatively prime p-adic entire functions of several variables. In this thesis we will also prove a few generalizations of Buium's results that he used in order to prove his ABC Theorems for isotrivial abelian varieties, respectively with trace zero. We hope to be able to use these results in order to prove a version of an ABC Theorem for any abelian variety over a function field.","abstract_html":"In this dissertation we will prove some ABC Theorems, namely for relatively prime by pairs p-adic entire functions in one variable, for p-adic meromorphic functions in several variables without common factors, under the hypothesis that no subsum vanishes, and also for pairwise relatively prime p-adic entire functions of several variables. In this thesis we will also prove a few generalizations of Buium's results that he used in order to prove his ABC Theorems for isotrivial abelian varieties, respectively with trace zero. We hope to be able to use these results in order to prove a version of an ABC Theorem for any abelian variety over a function field.","abstract_has_math":false,"creators":["Toropu, Cristina"],"institution":null,"degree_name":"Mathematics","degree_level":"Doctoral","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Buium, Alexandr","Alexandru Buium","Charles Boyer","Michael Nakamaye","Gordon Heier"],"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":["ABC THEOREMS"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalrepository.unm.edu/math_etds/49"],"render_values":[{"text":"https://digitalrepository.unm.edu/math_etds/49","href":"https://digitalrepository.unm.edu/math_etds/49","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1928/24350","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","Michael Nakamaye","Gordon Heier"]},{"key":"dc:creator","label":"Author","values":["Toropu, Cristina"]}]},{"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":["ABC THEOREMS"]}]},{"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/1928/24350","https://digitalrepository.unm.edu/math_etds/49"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this dissertation we will prove some ABC Theorems, namely for relatively prime by pairs p-adic entire functions in one variable, for p-adic meromorphic functions in several variables without common factors, under the hypothesis that no subsum vanishes, and also for pairwise relatively prime p-adic entire functions of several variables. In this thesis we will also prove a few generalizations of Buium's results that he used in order to prove his ABC Theorems for isotrivial abelian varieties, respectively with trace zero. We hope to be able to use these results in order to prove a version of an ABC Theorem for any abelian variety over a function field."]},{"key":"dc:title","label":"Title","values":["ABC Theorems In The Functional Case"]}]}],"canonical_facts":{"dc:contributor":["Buium, Alexandr","Alexandru Buium","Charles Boyer","Michael Nakamaye","Gordon Heier"],"dc:creator":["Toropu, Cristina"],"dc:description.abstract":["In this dissertation we will prove some ABC Theorems, namely for relatively prime by pairs p-adic entire functions in one variable, for p-adic meromorphic functions in several variables without common factors, under the hypothesis that no subsum vanishes, and also for pairwise relatively prime p-adic entire functions of several variables. In this thesis we will also prove a few generalizations of Buium's results that he used in order to prove his ABC Theorems for isotrivial abelian varieties, respectively with trace zero. We hope to be able to use these results in order to prove a version of an ABC Theorem for any abelian variety over a function field."],"dc:identifier":["http://hdl.handle.net/1928/24350","https://digitalrepository.unm.edu/math_etds/49"],"dc:language":["English"],"dc:subject":["ABC THEOREMS"],"dc:title":["ABC Theorems In The Functional Case"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Doctoral","Dissertation"],"thesis:degree_name":["Mathematics"]},"updated_at":"2026-07-24T05:27:37Z"}