Hausdorff dimensions in Pierce expansions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913452960776192 |
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| author | Ahn, Min Woong |
| author_facet | Ahn, Min Woong |
| contents | The digits of Pierce expansion obey the law of large numbers, the central limit theorem, and the law of the iterated logarithm in the Lebesgue measure sense. We calculate the Hausdorff dimensions of the exceptional sets of each of the three laws. We further determine the Hausdorff dimensions of certain sets arising in Pierce expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14162 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hausdorff dimensions in Pierce expansions Ahn, Min Woong Number Theory Classical Analysis and ODEs Primary 11K55, Secondary 28A80 The digits of Pierce expansion obey the law of large numbers, the central limit theorem, and the law of the iterated logarithm in the Lebesgue measure sense. We calculate the Hausdorff dimensions of the exceptional sets of each of the three laws. We further determine the Hausdorff dimensions of certain sets arising in Pierce expansions. |
| title | Hausdorff dimensions in Pierce expansions |
| topic | Number Theory Classical Analysis and ODEs Primary 11K55, Secondary 28A80 |
| url | https://arxiv.org/abs/2304.14162 |