2026/108/3-4 (8)
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DOI: 10.5486/PMD.2026.10276
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pp. 419-430
Solubility of additive quartic forms over $\mathbb{Q}_2(\sqrt{-5})$
Authors:
Geovane Matheus Lemes Andrade 
and Drew Duncan
Abstract:
We prove that the minimum number of variables $\Gamma^{*}(d,K)$ which guarantees a nontrivial zero for every additive form of degree $d=4$ over the $2$-adic field $K=\mathbb{Q}_2(\sqrt{-5})$ is $9$.
Keywords: forms in many variables, additive forms, $p$-adic fields, ramified extensions
Mathematics Subject Classification: 11D72, 11D88, 11E76