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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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2012
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152235 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1522352019-06-10T01:26:15Z Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers Zhykharyeva, Yu. Pratsiovytyi, M. 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. 2012 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/152235 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Zhykharyeva, Yu. Pratsiovytyi, M. |
| spellingShingle |
Zhykharyeva, Yu. Pratsiovytyi, M. Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers Algebra and Discrete Mathematics |
| author_facet |
Zhykharyeva, Yu. Pratsiovytyi, M. |
| author_sort |
Zhykharyeva, Yu. |
| title |
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_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_sort |
expansions of numbers in positive lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152235 |
| 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. |
| series |
Algebra and Discrete Mathematics |
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2023-05-20T17:37:49Z |
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