Sums of three cubes over a function field
| Autor: | Browning, Tim, Glas, Jakob, Wang, Victor Y. |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 57 pages |
| Databáze: | arXiv |
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