A nonabelian circle method
| Autor: | Arala, Nuno, Getz, Jayce R., Hou, Jiaqi, Hsu, Chun-Hsien, Li, Huajie, Wang, Victor Y. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We count integral quaternion zeros of $\gamma_1^2 \pm \dots \pm \gamma_n^2$, giving an asymptotic when $n\ge 9$, and a likely near-optimal bound when $n=8$. To do so, we introduce a new, nonabelian delta symbol method, which is of independent interest. Our asymptotic at height $X$ takes the form $cX^{4n-8} + O(X^{3n+\varepsilon})$ for suitable $c \in \mathbb{C}$ and any $\varepsilon>0.$ We construct special subvarieties implying that, in general, $3n+\varepsilon$ can be at best improved to $3n-2.$ Comment: 66 pages, 0 figures. Added supplementary material by Arala, Hou, Hsu, Li, and Wang |
| Databáze: | arXiv |
| Externí odkaz: |
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