Sums of three cubes over a function field
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910326302179328 |
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| author | Browning, Tim Glas, Jakob Wang, Victor Y. |
| author_facet | Browning, Tim Glas, Jakob Wang, Victor Y. |
| contents | We use a function field version of the circle method to prove that a positive proportion of elements in $\mathbb{F}_q[t]$ are representable as a sum of three cubes of minimal degree from $\mathbb{F}_q[t]$, assuming a suitable form of the Ratios Conjecture and that the characteristic is greater than 3. The analogue of this conjecture for quadratic Dirichlet $L$-functions is known for large fixed $q$, via recent developments in homological stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07146 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sums of three cubes over a function field Browning, Tim Glas, Jakob Wang, Victor Y. Number Theory Algebraic Geometry 11D45 (11D25, 11G40, 11M50, 11P55, 11T55) We use a function field version of the circle method to prove that a positive proportion of elements in $\mathbb{F}_q[t]$ are representable as a sum of three cubes of minimal degree from $\mathbb{F}_q[t]$, assuming a suitable form of the Ratios Conjecture and that the characteristic is greater than 3. The analogue of this conjecture for quadratic Dirichlet $L$-functions is known for large fixed $q$, via recent developments in homological stability. |
| title | Sums of three cubes over a function field |
| topic | Number Theory Algebraic Geometry 11D45 (11D25, 11G40, 11M50, 11P55, 11T55) |
| url | https://arxiv.org/abs/2402.07146 |