English

Solubility of Additive Sextic Forms over $\mathbb{Q}_2(\sqrt{-1})$ and $\mathbb{Q}_2(\sqrt{-5})$

Number Theory 2021-01-01 v2

Abstract

Michael Knapp, in a previous work, conjectured that every additive sextic form over Q2(1)\mathbb{Q}_2(\sqrt{-1}) and Q2(5)\mathbb{Q}_2(\sqrt{-5}) in seven variables has a nontrivial zero. In this paper, we show that this conjecture is true, establishing that Γ(6,Q2(1))=Γ(6,Q2(5))=7\Gamma^*(6, \mathbb{Q}_2(\sqrt{-1})) = \Gamma^*(6, \mathbb{Q}_2(\sqrt{-5})) = 7 .

Keywords

Cite

@article{arxiv.2005.09770,
  title  = {Solubility of Additive Sextic Forms over $\mathbb{Q}_2(\sqrt{-1})$ and $\mathbb{Q}_2(\sqrt{-5})$},
  author = {Drew Duncan and David B. Leep},
  journal= {arXiv preprint arXiv:2005.09770},
  year   = {2021}
}