Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers

• Datum: 2018
• Hauptverfasser: Zhykharyeva, Yulia, Pratsiovytyi, Mykola
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2018
• Schlagworte: Luroth series; \(L\)-representation; cylinder; semicylinder; shift operator; random variable defined by \(L\)-representation; fractal,Hausdorff-Besicovitch dimension; 11K55
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/716
• Назва журналу: Algebra and Discrete Mathematics

We describe the geometry of representation of numbers belonging to \((0,1]\) by the positive Lüroth series, i.e., special series whose terms are reciprocal of positive integers. We establish the geometrical meaning of digits, give properties of cylinders, semicylinders and tail sets, metric relation...