Solubility of additive quartic forms over ℚ2(−1)

In a previous work, Drew Duncan and David B. Leep conjectured that the minimum number of variables required to guarantee a nontrivial zero for every additive quartic form over [Formula: see text] is 11. In this paper, we confirm their conjecture, establishing that [Formula: see text].

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Publication Details

Journal
International Journal of Number Theory
Published
2025-11-21
DOI
https://doi.org/10.1142/s1793042126500405
Primary Topic
Algebraic Geometry and Number Theory
Type
article
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article

Solubility of additive quartic forms over ℚ2(−1)

Geovane Matheus Lemes Andrade
International Journal of Number Theory
Algebraic Geometry and Number Theory
article

Solubility of additive quartic forms over ℚ2(−1)

Geovane Matheus Lemes Andrade
article en

Abstract

In a previous work, Drew Duncan and David B. Leep conjectured that the minimum number of variables required to guarantee a nontrivial zero for every additive quartic form over [Formula: see text] is 11. In this paper, we confirm their conjecture, establishing that [Formula: see text].

International Journal of Number TheoryVol. 22(04)
Universidade de Brasília (BR)
Openalex Percentile: Top 58%
Algebraic Geometry and Number Theory
DOISourceOpenAlex
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Solubility of additive quartic forms over ℚ2(−1) — Geovane Matheus Lemes Andrade · International Journal of Number Theory (2025) | TGRS Research Map | TGRS