Cyclic sextic trinomials x6 + Ax + B

Andrew Bremner, Blair K. Spearman

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)161-167
Number of pages7
JournalInternational Journal of Number Theory
Volume6
Issue number1
DOIs
StatePublished - Feb 2010

Keywords

  • Galois group
  • Genus two curve
  • Sextic field
  • Trinomial

ASJC Scopus subject areas

  • Algebra and Number Theory

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