| Title:
|
Normal number constructions for Cantor series with slowly growing bases (English) |
| Author:
|
Airey, Dylan |
| Author:
|
Mance, Bill |
| Author:
|
Vandehey, Joseph |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
465-480 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $Q=(q_n)_{n=1}^\infty $ be a sequence of bases with $q_i\ge 2$. In the case when the $q_i$ are slowly growing and satisfy some additional weak conditions, we provide a construction of a number whose $Q$-Cantor series expansion is both $Q$-normal and $Q$-distribution normal. Moreover, this construction will result in a computable number provided we have some additional conditions on the computability of $Q$, and from this construction we can provide computable constructions of numbers with atypical normality properties. (English) |
| Keyword:
|
Cantor series |
| Keyword:
|
normal number |
| MSC:
|
11A63 |
| MSC:
|
11K16 |
| idZBL:
|
Zbl 06604480 |
| idMR:
|
MR3519615 |
| DOI:
|
10.1007/s10587-016-0269-7 |
| . |
| Date available:
|
2016-06-16T12:56:11Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145737 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
