Solubility of Additive Sextic Forms over ℚ₂(√(-1)) and ℚ₂(√(-5))

2020/05/19 by Drew Duncan, Duncan, Drew, David B. Leep +1 · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.2005.09770

arxiv created 2020/12/31 · arxiv updated 2021/01/01

Abstract

Michael Knapp, in a previous work, conjectured that every additive sextic form over ℚ₂(√(-1)) and ℚ₂(√(-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 .

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