{"id":{"repo_id":"passau-thes","oai_identifier":"oai:kobv.de-opus4-uni-passau:1567"},"canonical_url":"https://search.dev.ndltd.org/etd/passau-thes/oai:kobv.de-opus4-uni-passau:1567","repository":{"repo_id":"passau-thes","name":"Universität Passau","base_url":"https://opus4.kobv.de/opus4-uni-passau/oai"},"display":{"title":"The Asymptotic Behavior of Birkhoff- and Lacunary Sums","abstract":"This doctoral thesis consists of three independently published research articles on the asymptoic behaviour of Lacunary- and Birkhoff sums. The former are sums formed by periodic functions and exponentially growing sequences of natural numbers. The corresponding summands often exhibit behavior typical of independent and identically distributed random variables. The methods used are of an analytical and probabilistic nature. The Birkhoff sums considered in this work are generated by the Kronecker sequence and by discontinuous functions. The methods employed are from the field of metric number theory, specifically classical results from continued fraction theory are utilized.","abstract_html":"This doctoral thesis consists of three independently published research articles on the asymptoic behaviour of Lacunary- and Birkhoff sums. The former are sums formed by periodic functions and exponentially growing sequences of natural numbers. The corresponding summands often exhibit behavior typical of independent and identically distributed random variables. The methods used are of an analytical and probabilistic nature. The Birkhoff sums considered in this work are generated by the Kronecker sequence and by discontinuous functions. The methods employed are from the field of metric number theory, specifically classical results from continued fraction theory are utilized.","abstract_has_math":false,"creators":["Frühwirth, Lorenz"],"institution":"Universität Passau","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Prochno, Joscha","Aistleitner, Christoph"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-04-01","date_published":"2025-04-01","updated_at":"2026-07-24T03:45:10Z","subjects":[],"languages":[],"rights":["Creative Commons - CC BY - Namensnennung 4.0 International"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1567","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Prochno, Joscha","Aistleitner, Christoph"]},{"key":"dc:creator","label":"Author","values":["Frühwirth, Lorenz"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universität Passau"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Passau"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Creative Commons - CC BY - Namensnennung 4.0 International"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This doctoral thesis consists of three independently published research articles on the asymptoic behaviour of Lacunary- and Birkhoff sums. The former are sums formed by periodic functions and exponentially growing sequences of natural numbers. The corresponding summands often exhibit behavior typical of independent and identically distributed random variables. The methods used are of an analytical and probabilistic nature. The Birkhoff sums considered in this work are generated by the Kronecker sequence and by discontinuous functions. The methods employed are from the field of metric number theory, specifically classical results from continued fraction theory are utilized."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The Asymptotic Behavior of Birkhoff- and Lacunary Sums"]}]}],"canonical_facts":{"dc:contributor":["Prochno, Joscha","Aistleitner, Christoph"],"dc:creator":["Frühwirth, Lorenz"],"dc:description.abstract":["This doctoral thesis consists of three independently published research articles on the asymptoic behaviour of Lacunary- and Birkhoff sums. The former are sums formed by periodic functions and exponentially growing sequences of natural numbers. The corresponding summands often exhibit behavior typical of independent and identically distributed random variables. The methods used are of an analytical and probabilistic nature. The Birkhoff sums considered in this work are generated by the Kronecker sequence and by discontinuous functions. The methods employed are from the field of metric number theory, specifically classical results from continued fraction theory are utilized."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Passau"],"dc:rights":["Creative Commons - CC BY - Namensnennung 4.0 International"],"dc:title":["The Asymptotic Behavior of Birkhoff- and Lacunary Sums"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Passau"]},"updated_at":"2026-07-24T03:45:10Z"}