o-Polynomials and Explicit Formula for o-Monomials Oertel, Alexander , 2001- (VerfasserIn) Kyureghyan, Gohar M. , 1974- (AkademischeR BetreuerIn) Krompholz, Lucas (AkademischeR BetreuerIn) Universität Rostock (Grad-verleihende Institution) Universität Rostock Mathematisch-Naturwissenschaftliche Fakultät (Grad-verleihende Institution) Text theses Text Hochschulschrift 2024 2024 eng electronic resourceremoteComputermedienOnline-Ressourceapplication/pdf1 Online-Ressource (I, 86 Seiten) Illustrationen Hyperovals in finite Desarguesian planes of even order q are sets of q+2 points, of which no three are collinear. By association with o-polynomials over binary finite fields, they can be studied algebraically. In this thesis o-polynomials and an equivalence relation based on the equivalence under collineations of the plane are investigated. A second topic is the connection to 2-to-1 polynomials, where explicit formulas for the known o-monomials allow the construction of 2-to-1 binomials. Finally, some generalizations to fields of odd characteristic are made as well.<eng> Open Access Namensnennung 4.0 International vorgelegt von Alexander Oertel GutachterInnen: Gohar Kyureghyan (Institut für Mathematik, Universität Rostock) ; Lucas Krompholz (Institut für Mathematik, Universität Rostock) Masterarbeit Universität Rostock 2024 510 516 510 https://purl.uni-rostock.de/rosdok/id00004695 https://doi.org/10.18453/rosdok_id00004695 https://nbn-resolving.org/urn:nbn:de:gbv:28-rosdok_id00004695-4 https://d-nb.info/1349335126/34 urn:nbn:de:gbv:28-rosdok_id00004695-4 doi: 10.18453/rosdok_id00004695 oclc: 1468601708 ppn: (DE-627)1908457368