Solubility of Additive Quartic Forms over Ramified Quadratic Extensions of ℚ₂

2021/12/20 by Drew Duncan, Duncan, Drew, David B. Leep +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.2112.10854

arXiv admin note: text overlap with arXiv:2010.06833

arxiv created 2021/12/20 · arxiv updated 2021/12/22

Abstract

We determine the minimal number of variables Γ^*(d, K) which guarantees a nontrivial solution for every additive form of degree d=4 over the four ramified quadratic extensions ℚ₂(√(2)), ℚ₂(√(10)), ℚ₂(√(-2)), ℚ₂(√(-10)) of ℚ₂. In all four fields, we prove that Γ^*(4,K) = 11. This is the first example of such a computation for a proper extension of ℚ_p where the degree is a power of p greater than p.

Citations

• Solubility of Additive Forms of Twice Odd Degree over Ramified Quadratic Extensions of ℚ₂

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