| Title:
|
The fractional dimensional theory in Lüroth expansion (English) |
| Author:
|
Shen, Luming |
| Author:
|
Fang, Kui |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
795-807 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is well known that every $x\in (0,1]$ can be expanded to an infinite Lüroth series in the form of $$x=\frac {1}{d_1(x)}+\cdots +\frac {1}{d_1(x)(d_1(x)-1)\cdots d_{n-1}(x)(d_{n-1}(x)-1)d_n(x)}+\cdots , $$ where $d_n(x)\geq 2$ for all $n\geq 1$. In this paper, sets of points with some restrictions on the digits in Lüroth series expansions are considered. Mainly, the Hausdorff dimensions of the Cantor sets $$ F_{\phi }=\{x\in (0,1]\colon d_n(x)\geq \phi (n), \ \forall n\geq 1\} $$are completely determined, where $\phi $ is an integer-valued function defined on $\mathbb N$, and $\phi (n)\to \infty $ as $n\to \infty $. (English) |
| Keyword:
|
Lüroth series |
| Keyword:
|
Cantor set |
| Keyword:
|
Hausdorff dimension |
| MSC:
|
11K55 |
| MSC:
|
28A78 |
| MSC:
|
28A80 |
| idZBL:
|
Zbl 1249.11084 |
| idMR:
|
MR2853093 |
| DOI:
|
10.1007/s10587-011-0028-8 |
| . |
| Date available:
|
2011-09-22T14:48:05Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141640 |
| . |
| Reference:
|
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| . |
