Powered numbers in short intervals II
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914241655603200 |
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| author | Chan, Tsz Ho |
| author_facet | Chan, Tsz Ho |
| contents | In this article, we derive better results concerning powered numbers in short intervals, both unconditionally and conditionally on the $abc$-conjecture. We make use of sieve method, a polynomial identity, and a recent breakthrough result on density of sets with no $k$-term arithmetic progression. In the process, we study integers over short intervals that have with a big smooth divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Powered numbers in short intervals II Chan, Tsz Ho Number Theory 11N25 In this article, we derive better results concerning powered numbers in short intervals, both unconditionally and conditionally on the $abc$-conjecture. We make use of sieve method, a polynomial identity, and a recent breakthrough result on density of sets with no $k$-term arithmetic progression. In the process, we study integers over short intervals that have with a big smooth divisor. |
| title | Powered numbers in short intervals II |
| topic | Number Theory 11N25 |
| url | https://arxiv.org/abs/2406.10014 |