Solubility of Additive Forms of Twice Odd Degree over Totally Ramified Extensions of $\mathbb{Q}_2$

Abstract

We prove that an additive form of degree $d=2m$, $m$ odd over any totally ramified extension of $\mathbb{Q}_2$ has a nontrivial zero if the number of variables $s$ satisifies $s \ge \frac{d^2}{4} + 3d + 1$.