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

Abstract

We determine the minimal number of variables Γ * (d, K) which guarantees a nontrivial solution for every additive form of degree d = 2m, m odd, m ≥ 3 over the six ramified quadratic extensions of Q2. We prove that ifThe case d = 6 was previously known.