Solubility of Additive Forms of Twice Odd Degree over Totally Ramified Extensions of ℚ₂

2022/12/15 by Duncan, Drew
#11D72 #11D88 #11E76 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2212.07604

Abstract

We prove that an additive form of degree d=2m, m odd over any totally ramified extension of ℚ₂ has a nontrivial zero if the number of variables s satisifies s ≥ (d²)/(4) + 3d + 1.

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