Solubility of Additive Forms of Twice Odd Degree over Ramified Quadratic Extensions of $\mathbb{Q}_2$
| Autor: | Duncan, Drew, Leep, David B. |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | We determine the minimal number of variables $\Gamma^*(d, K)$ which guarantees a nontrivial solution for every additive form of degree $d=2m$, $m$ odd, $m \ge 3$ over the six ramified quadratic extensions of $\mathbb{Q}_2$. We prove that if $K$ is one of $\{\mathbb{Q}_2(\sqrt{2}), \mathbb{Q}_2(\sqrt{10}), \mathbb{Q}_2(\sqrt{-2}), \mathbb{Q}_2(\sqrt{-10})\}$, $\Gamma^*(d,K) = \frac{3}{2}d$, and if $K$ is one of $\{\mathbb{Q}_2(\sqrt{-1}), \mathbb{Q}_2(\sqrt{-5})\}$, $\Gamma^*(d,K) = d+1$. The case $d=6$ was previously known. Comment: arXiv admin note: text overlap with arXiv:2005.09770 |
| Databáze: | arXiv |
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