Numbers with three close factorizations and central lattice points on hyperbolas
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908442509180928 |
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| author | Chan, Tsz Ho |
| author_facet | Chan, Tsz Ho |
| contents | In this paper, we continue the study of three close factorizations of an integer and correct a mistake of a previous result. This turns out to be related to lattice points close to the center point $(\sqrt{N}, \sqrt{N})$ of the hyperbola $x y = N$. We establish optimal lower bounds for $L^1$-distance between these lattice points and the center. We also give some good examples based on polynomials and Pell equations more systematically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numbers with three close factorizations and central lattice points on hyperbolas Chan, Tsz Ho Number Theory In this paper, we continue the study of three close factorizations of an integer and correct a mistake of a previous result. This turns out to be related to lattice points close to the center point $(\sqrt{N}, \sqrt{N})$ of the hyperbola $x y = N$. We establish optimal lower bounds for $L^1$-distance between these lattice points and the center. We also give some good examples based on polynomials and Pell equations more systematically. |
| title | Numbers with three close factorizations and central lattice points on hyperbolas |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.07094 |