Solubility of additive quartic forms over ramified quadratic extensions of ℚ2

Abstract

In this paper, we determine the minimal number of variables [Formula: see text] which guarantees a nontrivial solution for every additive form of degree [Formula: see text] over the four ramified quadratic extensions [Formula: see text] of [Formula: see text]. In all four fields, we prove that [Formula: see text]. This is the first example of such a computation for a proper ramified extension of [Formula: see text] where the degree is a power of [Formula: see text] greater than [Formula: see text].