Transformations and functions that preserve the asymptotic mean of digits in the ternary representation of a number
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arXiv
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| Format: | Preprint |
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2026
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| author | Pratsiovytyi, M. V. Klymchuk, S. O. Makarchuk, O. P. |
| author_facet | Pratsiovytyi, M. V. Klymchuk, S. O. Makarchuk, O. P. |
| contents | In the paper we study transformations of the interval $[0;1)$ and functions that preserve the asymptotic mean $r$ of the digits in the $s$--adic representation of a number $x$, $$r(x)=\lim\limits_{n\to\infty}\frac{1}{n}\sum\limits^{n}_{i=1}α_i(x)$$ specify the necessary and sufficient conditions for a transformation to belong to this class |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04871 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transformations and functions that preserve the asymptotic mean of digits in the ternary representation of a number Pratsiovytyi, M. V. Klymchuk, S. O. Makarchuk, O. P. Number Theory Functional Analysis 11K50, 26A27, 26A30 In the paper we study transformations of the interval $[0;1)$ and functions that preserve the asymptotic mean $r$ of the digits in the $s$--adic representation of a number $x$, $$r(x)=\lim\limits_{n\to\infty}\frac{1}{n}\sum\limits^{n}_{i=1}α_i(x)$$ specify the necessary and sufficient conditions for a transformation to belong to this class |
| title | Transformations and functions that preserve the asymptotic mean of digits in the ternary representation of a number |
| topic | Number Theory Functional Analysis 11K50, 26A27, 26A30 |
| url | https://arxiv.org/abs/2603.04871 |