Some quartic number fields containing an imaginary quadratic subfield

• Autorzy: Stéphane R. Louboutin
• Języki publikacji: EN

Abstrakty

EN

Let ε be a quartic algebraic unit. We give necessary and sufficient conditions for (i) the quartic number field K = ℚ(ε) to contain an imaginary quadratic subfield, and (ii) for the ring of algebraic integers of K to be equal to ℤ[ε]. We also prove that the class number of such K's goes to infinity effectively with the discriminant of K.

Kategorie tematyczne

• 11R16: Cubic and quartic extensions
• 11R29: Class numbers, class groups, discriminants
• 11R27: Units and factorization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 122
• Numer: 1
• Strony: 139-148

Daty

wydano

2011

Twórcy

autor

Stéphane R. Louboutin

• Institut de Mathématiques de Luminy, UMR 6206, 163, avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France

Identyfikatory

DOI

10.4064/cm122-1-13