Optimal sums of three cubes in $\mathbb{F}_q[t]$
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909784673878016 |
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| author | Browning, Tim Glas, Jakob Wang, Victor Y. |
| author_facet | Browning, Tim Glas, Jakob Wang, Victor Y. |
| contents | We use the circle method to prove that a density 1 of elements in $\mathbb{F}_q[t]$ are representable as a sum of three cubes of essentially minimal degree from $\mathbb{F}_q[t]$, assuming the Ratios Conjecture and that the characteristic is bigger than 3. Roughly speaking, to do so, we upgrade an order of magnitude result to a full asymptotic formula that was conjectured by Hooley in the number field setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal sums of three cubes in $\mathbb{F}_q[t]$ Browning, Tim Glas, Jakob Wang, Victor Y. Number Theory 11D45 (11D25, 11G40, 11M50, 11P55, 11T55) We use the circle method to prove that a density 1 of elements in $\mathbb{F}_q[t]$ are representable as a sum of three cubes of essentially minimal degree from $\mathbb{F}_q[t]$, assuming the Ratios Conjecture and that the characteristic is bigger than 3. Roughly speaking, to do so, we upgrade an order of magnitude result to a full asymptotic formula that was conjectured by Hooley in the number field setting. |
| title | Optimal sums of three cubes in $\mathbb{F}_q[t]$ |
| topic | Number Theory 11D45 (11D25, 11G40, 11M50, 11P55, 11T55) |
| url | https://arxiv.org/abs/2408.03668 |