Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers
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| Creator |
Zhykharyeva, Yu.
Pratsiovytyi, M. |
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| 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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| Date |
2019-06-09T06:04:06Z
2019-06-09T06:04:06Z 2012 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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