Solubility of Additive Forms of Twice Odd Degree over Q2(√5)

Drew Duncan; David B. Leep

doi:10.5802/jtnb.1279

Solubility of Additive Forms of Twice Odd Degree over Q₂(^√5)

Drew Duncan, David B. Leep

Mathematics

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

Abstract

We prove that an additive form of degree d = 2m, m odd, m ≥ 3, over the unramified quadratic extension ℚ₂(^√5) has a nontrivial zero if the number of variables s satisifies s ≥ 4d+1. If 3 ∤ d, then there exists a nontrivial zero if s ≥3/2d + 1, this bound being optimal. We give examples of forms in 3d variables without a nontrivial zero in case that 3 | d.

Original language	English
Pages (from-to)	293-309
Number of pages	17
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	36
Issue number	1
DOIs	https://doi.org/10.5802/jtnb.1279
State	Published - 2024

Bibliographical note

Publisher Copyright:
© Les auteurs, 2024.

Keywords

additive forms
Forms in many variables
p-adic fields
unramified extension

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.5802/jtnb.1279

Cite this

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