Solubility of Additive Forms of Twice Odd Degree over $\mathbb{Q}_2(\sqrt{5})$
| Autor: | Duncan, Drew, Leep, David B. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove that an additive form of degree $d=2m$, $m$ odd, $m\ge3$, over the unramified quadratic extension $\mathbb{Q}_2(\sqrt{5})$ has a nontrivial zero if the number of variables $s$ satisifies $s \ge 4d+1$. If $3 \nmid d$, then there exists a nontrivial zero if $s \ge \frac{3}{2}d + 1$, this bound being optimal. We give examples of forms in $3d$ variables without a nontrivial zero in case that $3 \mid d$. |
| Databáze: | arXiv |
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