On Vu's restricted box estimate in Waring's problem
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917496159731712 |
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| author | Táfula, Christian |
| author_facet | Táfula, Christian |
| contents | In 2000, Vu proved that the number of solutions of $x_1^k + \cdots + x_s^k = N$ in an arbitrary box satisfies the expected Hardy--Littlewood upper bound with a power-saving error term, for $s \geq O(8^k k^3)$. We show that one may take $s\geq k^2 - k + O(\sqrt{k})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15067 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Vu's restricted box estimate in Waring's problem Táfula, Christian Number Theory 11P05, 11P55 In 2000, Vu proved that the number of solutions of $x_1^k + \cdots + x_s^k = N$ in an arbitrary box satisfies the expected Hardy--Littlewood upper bound with a power-saving error term, for $s \geq O(8^k k^3)$. We show that one may take $s\geq k^2 - k + O(\sqrt{k})$. |
| title | On Vu's restricted box estimate in Waring's problem |
| topic | Number Theory 11P05, 11P55 |
| url | https://arxiv.org/abs/2605.15067 |