Convergence exponent of Pierce expansion digit sequences
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912463162703872 |
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| author | Ahn, Min Woong |
| author_facet | Ahn, Min Woong |
| contents | In this paper, we investigate the convergence exponent of Pierce expansion digit sequences. We explore some basic properties of the convergence exponent as a real-valued function defined on the closed unit interval, as well as those of the level sets of the function. Additionally, we further study subsets of the closed unit interval on which the series of positive $s$th powers of the reciprocals of the Pierce expansion digits diverges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01722 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence exponent of Pierce expansion digit sequences Ahn, Min Woong Number Theory Classical Analysis and ODEs General Topology Primary 26A21, Secondary 11K55, 28A80, 40A05, 54E52 In this paper, we investigate the convergence exponent of Pierce expansion digit sequences. We explore some basic properties of the convergence exponent as a real-valued function defined on the closed unit interval, as well as those of the level sets of the function. Additionally, we further study subsets of the closed unit interval on which the series of positive $s$th powers of the reciprocals of the Pierce expansion digits diverges. |
| title | Convergence exponent of Pierce expansion digit sequences |
| topic | Number Theory Classical Analysis and ODEs General Topology Primary 26A21, Secondary 11K55, 28A80, 40A05, 54E52 |
| url | https://arxiv.org/abs/2309.01722 |