On the $abc$ and the $abcd$ conjectures
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910476716212224 |
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| author | Pasten, Hector Sepúlveda-Manzo, Rocío |
| author_facet | Pasten, Hector Sepúlveda-Manzo, Rocío |
| contents | We revisit a subexponential bound for the $abc$ conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the $4$-terms $abc$ conjecture under a suitable hypothesis on the size of the variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05083 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $abc$ and the $abcd$ conjectures Pasten, Hector Sepúlveda-Manzo, Rocío Number Theory Primary: 11D75, Secondary: 11J25, 11J97, 11J86 We revisit a subexponential bound for the $abc$ conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the $4$-terms $abc$ conjecture under a suitable hypothesis on the size of the variables. |
| title | On the $abc$ and the $abcd$ conjectures |
| topic | Number Theory Primary: 11D75, Secondary: 11J25, 11J97, 11J86 |
| url | https://arxiv.org/abs/2406.05083 |