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 $s\ge \frac{d^2}{4}+3d+1$.

arXiv admin note: text overlap with arXiv:2207.09556