Solubility of additive forms of twice odd degree over totally ramified extensions of Q 2 $\mathbb {Q}_2$

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-07-22 DOI:10.1112/blms.13120

Drew Duncan

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引用次数: 0

Abstract

We prove that an additive form of degree $d = 2 m$ , $m$ odd over any totally ramified extension of $Q_{2}$ has a nontrivial zero if the number of variables $s$ satisfies $s ⩾ \frac{d^{2}}{4} + 3 d + 1$ .