Solubility of additive sextic forms over Q2(√−1) and Q2(√−5)(Formula Presented)

Drew Duncan; David B. Leep

doi:10.5486/PMD.2021.8973

Solubility of additive sextic forms over Q₂(^√−1) and Q₂(^√−5)(Formula Presented)

Drew Duncan
, David B. Leep

Mathematics

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

4 Scopus citations

Abstract

Michael Knapp, in a previous work, conjectured that every additive sextic form over Q2(^√−1) and Q2(^√−5)(Formula Presented)in seven variables has a nontrivial zero. In this paper, we show that this conjecture is true, establishing that Γ^*(6,Q2(^√−1)) = Γ^*(6,Q2(^√−5)) = 7.

Original language	English
Pages (from-to)	431-446
Number of pages	16
Journal	Publicationes Mathematicae Debrecen
Volume	99
Issue number	3-4
DOIs	https://doi.org/10.5486/PMD.2021.8973
State	Published - 2021

Bibliographical note

Publisher Copyright:
© 2021 University of Debrecen, Institute of Mathematics. All rights reserved.

Keywords

Diophantine equations
forms in many variables

ASJC Scopus subject areas

General Mathematics

Access to Document

10.5486/PMD.2021.8973

Cite this

@article{61caed58f7364d258c58103affa7ca04,

title = "Solubility of additive sextic forms over Q2(√−1) and Q2(√−5)(Formula Presented)",

abstract = "Michael Knapp, in a previous work, conjectured that every additive sextic form over Q2(√−1) and Q2(√−5)(Formula Presented)in seven variables has a nontrivial zero. In this paper, we show that this conjecture is true, establishing that Γ*(6,Q2(√−1)) = Γ*(6,Q2(√−5)) = 7.",

keywords = "Diophantine equations, forms in many variables",

author = "Drew Duncan and Leep, \{David B.\}",

year = "2021",

doi = "10.5486/PMD.2021.8973",

language = "English",

volume = "99",

pages = "431--446",

journal = "Publicationes Mathematicae Debrecen",

issn = "0033-3883",

publisher = "Institute of Mathematics, University of Debrecen",

number = "3-4",

}

TY - JOUR

T1 - Solubility of additive sextic forms over Q2(√−1) and Q2(√−5)(Formula Presented)

AU - Duncan, Drew

AU - Leep, David B.

PY - 2021

Y1 - 2021

N2 - Michael Knapp, in a previous work, conjectured that every additive sextic form over Q2(√−1) and Q2(√−5)(Formula Presented)in seven variables has a nontrivial zero. In this paper, we show that this conjecture is true, establishing that Γ*(6,Q2(√−1)) = Γ*(6,Q2(√−5)) = 7.

AB - Michael Knapp, in a previous work, conjectured that every additive sextic form over Q2(√−1) and Q2(√−5)(Formula Presented)in seven variables has a nontrivial zero. In this paper, we show that this conjecture is true, establishing that Γ*(6,Q2(√−1)) = Γ*(6,Q2(√−5)) = 7.

KW - Diophantine equations

KW - forms in many variables

UR - https://www.scopus.com/pages/publications/85121719141

UR - https://www.scopus.com/pages/publications/85121719141#tab=citedBy

U2 - 10.5486/PMD.2021.8973

DO - 10.5486/PMD.2021.8973

M3 - Article

AN - SCOPUS:85121719141

SN - 0033-3883

VL - 99

SP - 431

EP - 446

JO - Publicationes Mathematicae Debrecen

JF - Publicationes Mathematicae Debrecen

IS - 3-4

ER -