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- Title
Solubility of additive quartic forms over ramified quadratic extensions of ℚ2.
- Authors
Duncan, Drew; Leep, David B.
- Abstract
In this paper, 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 ℚ 2 (2) , ℚ 2 (1 0) , ℚ 2 (− 2) , ℚ 2 (− 1 0) of ℚ 2 . In all four fields, we prove that Γ ∗ (4 , K) = 1 1. This is the first example of such a computation for a proper ramified extension of ℚ p where the degree is a power of p greater than p.
- Subjects
SOLUBILITY; ADDITIVES
- Publication
International Journal of Number Theory, 2022, Vol 18, Issue 10, p2265
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042122501159