{"id":{"repo_id":"lsu-thes","oai_identifier":"oai:repository.lsu.edu:gradschool_dissertations-1728"},"canonical_url":"https://search.dev.ndltd.org/etd/lsu-thes/oai:repository.lsu.edu:gradschool_dissertations-1728","repository":{"repo_id":"lsu-thes","name":"Lousiana State University","base_url":"https://repository.lsu.edu/do/oai/"},"display":{"title":"A numerical investigation of Apéry-like recursions and related Picard-Fuchs equations","abstract":"In this work we investigate a generalization of a recursion which was used by Apery in his proof of irrationality of the zeta function values at 2 and 3. It is a continuation of the work of Zagier , who considered generalization of the first equation and numerically investigated it. The study is made for two generalizations of the second equation, one used the mirror symmetry idea from the theory of Calabi-Yau varieties and another worked with recursion. There were discovered connections between them.","abstract_html":"In this work we investigate a generalization of a recursion which was used by Apery in his proof of irrationality of the zeta function values at 2 and 3. It is a continuation of the work of Zagier , who considered generalization of the first equation and numerically investigated it. The study is made for two generalizations of the second equation, one used the mirror symmetry idea from the theory of Calabi-Yau varieties and another worked with recursion. There were discovered connections between them.","abstract_has_math":false,"creators":["Bakhova, Maiia J."],"institution":"Mathematics","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Applied Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-01-01T08:00:00Z","date_published":"2012-01-01T08:00:00Z","updated_at":"2026-07-24T02:58:17Z","subjects":["Picard-Fuchs equations","numerical investigation of recursions","Verrill","Zagier","Apery"],"languages":[],"rights":["unrestricted","Release the entire work immediately for access worldwide."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-01312012-141528","https://repository.lsu.edu/gradschool_dissertations/729"],"render_values":[{"text":"etd-01312012-141528","href":null,"code":true},{"text":"https://repository.lsu.edu/gradschool_dissertations/729","href":"https://repository.lsu.edu/gradschool_dissertations/729","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.31390/gradschool_dissertations.729","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Bakhova, Maiia J."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-12-02"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-05-12T23:09:47Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Applied Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Picard-Fuchs equations","numerical investigation of recursions","Verrill","Zagier","Apery"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","Release the entire work immediately for access worldwide."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-01312012-141528","10.31390/gradschool_dissertations.729","https://repository.lsu.edu/gradschool_dissertations/729"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this work we investigate a generalization of a recursion which was used by Apery in his proof of irrationality of the zeta function values at 2 and 3. It is a continuation of the work of Zagier , who considered generalization of the first equation and numerically investigated it. The study is made for two generalizations of the second equation, one used the mirror symmetry idea from the theory of Calabi-Yau varieties and another worked with recursion. There were discovered connections between them."]},{"key":"dc:title","label":"Title","values":["A numerical investigation of Apéry-like recursions and related Picard-Fuchs equations"]}]}],"canonical_facts":{"dc:creator":["Bakhova, Maiia J."],"dc:date":["2011-12-02"],"dc:date.available":["2022-05-12T23:09:47Z"],"dc:description.abstract":["In this work we investigate a generalization of a recursion which was used by Apery in his proof of irrationality of the zeta function values at 2 and 3. It is a continuation of the work of Zagier , who considered generalization of the first equation and numerically investigated it. The study is made for two generalizations of the second equation, one used the mirror symmetry idea from the theory of Calabi-Yau varieties and another worked with recursion. There were discovered connections between them."],"dc:identifier":["etd-01312012-141528","10.31390/gradschool_dissertations.729","https://repository.lsu.edu/gradschool_dissertations/729"],"dc:rights":["unrestricted","Release the entire work immediately for access worldwide."],"dc:subject":["Picard-Fuchs equations","numerical investigation of recursions","Verrill","Zagier","Apery"],"dc:title":["A numerical investigation of Apéry-like recursions and related Picard-Fuchs equations"],"thesis:degree_discipline":["Applied Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Mathematics"]},"updated_at":"2026-07-24T02:58:17Z"}