Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers
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;...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2012 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152235 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862685858794045440 |
|---|---|
| author | Zhykharyeva, Yu. Pratsiovytyi, M. |
| author_facet | Zhykharyeva, Yu. Pratsiovytyi, M. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | 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; prove topological, metric and fractal properties of sets of numbers with restrictions on use of “digits”; show that for determination of Hausdorff-Besicovitch dimension of Borel set it is enough to use connected unions of cylindrical sets of the same rank. Some applications of L-representation to probabilistic theory of numbers are also considered.
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| first_indexed | 2025-12-07T16:01:58Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152235 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T16:01:58Z |
| publishDate | 2012 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Zhykharyeva, Yu. Pratsiovytyi, M. 2019-06-09T06:04:06Z 2019-06-09T06:04:06Z 2012 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. 1726-3255 2010 MSC:11K55. https://nasplib.isofts.kiev.ua/handle/123456789/152235 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; prove topological, metric and fractal properties of sets of numbers with restrictions on use of “digits”; show that for determination of Hausdorff-Besicovitch dimension of Borel set it is enough to use connected unions of cylindrical sets of the same rank. Some applications of L-representation to probabilistic theory of numbers are also considered. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers Article published earlier |
| spellingShingle | Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers Zhykharyeva, Yu. Pratsiovytyi, M. |
| title | Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| title_full | Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| title_fullStr | Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| title_full_unstemmed | Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| title_short | Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| title_sort | expansions of numbers in positive lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152235 |
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