Cyclic sextic trinomials x6 + Ax + B

Andrew Bremner; Blair K. Spearman

doi:10.1142/S1793042110002843

Cyclic sextic trinomials x⁶ + Ax + B

Andrew Bremner, Blair K. Spearman

Mathematical and Statistical Sciences, School of (SoMSS)

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

4 Scopus citations

Abstract

A correspondence is obtained between irreducible cyclic sextic trinomials x⁶ + Ax + B ∈ ℚ[x] and rational points on a genus two curve. This implies that up to scaling, x⁶ + 133x + 209 is the only cyclic sextic trinomial of the given type.

Original language	English (US)
Pages (from-to)	161-167
Number of pages	7
Journal	International Journal of Number Theory
Volume	6
Issue number	1
DOIs	https://doi.org/10.1142/S1793042110002843
State	Published - Feb 2010

Keywords

Galois group
Genus two curve
Sextic field
Trinomial

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1142/S1793042110002843

Cite this

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title = "Cyclic sextic trinomials x6 + Ax + B",

abstract = "A correspondence is obtained between irreducible cyclic sextic trinomials x6 + Ax + B ∈ ℚ[x] and rational points on a genus two curve. This implies that up to scaling, x6 + 133x + 209 is the only cyclic sextic trinomial of the given type.",

keywords = "Galois group, Genus two curve, Sextic field, Trinomial",

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AU - Spearman, Blair K.

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AB - A correspondence is obtained between irreducible cyclic sextic trinomials x6 + Ax + B ∈ ℚ[x] and rational points on a genus two curve. This implies that up to scaling, x6 + 133x + 209 is the only cyclic sextic trinomial of the given type.

KW - Galois group

KW - Genus two curve

KW - Sextic field

KW - Trinomial

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