2026-09-23T17:41:19Z https://opus4.kobv.de/opus4-uni-passau/oai

oai:kobv.de-opus4-uni-passau:1567 2025-08-13 bibliography:false doc-type:PhDThesis open_access ddc ddc:510

The Asymptotic Behavior of Birkhoff- and Lacunary Sums 0009-0005-5777-6883 Lorenz Frühwirth 510 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. Universität Passau Passau Innstrasse 29, 94032 Passau Joscha Prochno Christoph Aistleitner 2025-04-01 2025-04-14 PhDThesis Text urn:nbn:de:bvb:739-opus4-15677 application/pdf eng Creative Commons - CC BY - Namensnennung 4.0 International thesis.doctoral Universität Passau Passau 1 https://opus4.kobv.de/opus4-uni-passau/oai/container/index/docId/1567 https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1567