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

• Published in: Algebra and Discrete Mathematics
• Date: 2012
• ISSN: 1726-3255
• Main Authors: Zhykharyeva, Yu., Pratsiovytyi, M.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2012
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/152235
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers / Yu. Zhykharyeva, M. Pratsiovytyi // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 1. — С. 145–160. — Бібліогр.: 18 назв. — англ.

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 relations;...