On the fundamental units of some cubic orders generated by units

• Autorzy: Jun Ho Lee , Stéphane R. Louboutin
• Języki publikacji: EN

Abstrakty

EN

Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic polynomials are considered. We also improve upon and correct several previous results in the literature.

Kategorie tematyczne

• 11R16: Cubic and quartic extensions
• 11R27: Units and factorization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 165
• Numer: 3
• Strony: 283-299

Daty

wydano

2014

Twórcy

autor

Jun Ho Lee

• School of Mathematics, Korea Institute for, Advanced Study (KIAS), 85 Hoegiro, Dongdaemun-gu, Seoul 130-722, Republic of Korea

autor

Stéphane R. Louboutin

• Aix Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France

Identyfikatory

DOI

10.4064/aa165-3-7