Ratios of consecutive values of the divisor function
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866915585788477440 |
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| author | Eberhard, Sean |
| author_facet | Eberhard, Sean |
| contents | We show that the sequence of ratios $d(n+1) / d(n)$ of consecutive values of the divisor function attains every positive rational infinitely many times. This confirms a prediction of Erdős. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ratios of consecutive values of the divisor function Eberhard, Sean Number Theory We show that the sequence of ratios $d(n+1) / d(n)$ of consecutive values of the divisor function attains every positive rational infinitely many times. This confirms a prediction of Erdős. |
| title | Ratios of consecutive values of the divisor function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.00727 |