Solubility of additive quartic forms over ramified quadratic extensions of Q2

Drew Duncan; David B. Leep

doi:10.1142/S1793042122501159

Solubility of additive quartic forms over ramified quadratic extensions of Q₂

Drew Duncan, David B. Leep

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 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 ramified extension of ℚp where the degree is a power of p greater than p.

Original language	English
Pages (from-to)	2265-2278
Number of pages	14
Journal	International Journal of Number Theory
Volume	18
Issue number	10
DOIs	https://doi.org/10.1142/S1793042122501159
State	Published - Nov 1 2022

Bibliographical note

Publisher Copyright:
© 2022 World Scientific Publishing Company.

Keywords

Forms in many variables
additive forms
p -adic fields
ramified extensions

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1142/S1793042122501159

Cite this

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