Random Diophantine Equations in the Primes II
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866918499780132864 |
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| author | Holdridge, Philippa |
| author_facet | Holdridge, Philippa |
| contents | Let $d\ge 2$ and $n\ge d$ with $(d,n)\notin \{(2,2),(3,3)\}$. We consider homogeneous Diophantine equations of degree $d$ in $n+1$ variables and whether they have solutions in the primes. In particular, we show that a certain local-global principle holds for almost all such equations, following on from previous work of the author arXiv:2305.06306. We do this by adapting the methods of Browning, Le Boudec and Sawin (Annals, 2023). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_02137 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Random Diophantine Equations in the Primes II Holdridge, Philippa Number Theory 11D45, 11P21, 11P32 Let $d\ge 2$ and $n\ge d$ with $(d,n)\notin \{(2,2),(3,3)\}$. We consider homogeneous Diophantine equations of degree $d$ in $n+1$ variables and whether they have solutions in the primes. In particular, we show that a certain local-global principle holds for almost all such equations, following on from previous work of the author arXiv:2305.06306. We do this by adapting the methods of Browning, Le Boudec and Sawin (Annals, 2023). |
| title | Random Diophantine Equations in the Primes II |
| topic | Number Theory 11D45, 11P21, 11P32 |
| url | https://arxiv.org/abs/2310.02137 |