Counting cubic extensions with given quadratic resolvent

DOI10.1016/j.jalgebra.2010.08.027zbMath1239.11115arXiv1003.1869OpenAlexW1997976746MaRDI QIDQ630867

Anna Morra, Henri Cohen

Publication date: 22 March 2011

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.1869

zbMATH Keywords

Kummer theoryresolventsScholz reflection theoremcubic extensionsdiscriminant counting

Mathematics Subject Classification ID

Cubic and quartic extensions (11R16)

Related Items (10)

On the number of pure fields of prime degree ⋮ The shapes of pure cubic fields ⋮ Identities for field extensions generalizing the Ohno–Nakagawa relations ⋮ Construction of all cubic function fields of a given square-free discriminant ⋮ Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves ⋮ Shintani’s zeta function is not a finite sum of Euler products ⋮ Dirichlet series associated to cubic fields with given quadratic resolvent ⋮ Equidistribution of shapes of complex cubic fields of fixed quadratic resolvent ⋮ Dirichlet series associated to quartic fields with given cubic resolvent ⋮ Exact counting of $D_\ell $ number fields with given quadratic resolvent

Cites Work

• Unnamed Item
• Unnamed Item
• Cyclotomic extensions of number fields
• Density of discriminants of cubic extensions.
• Über die Beziehung der Klassenzahlen quadratischer Körper zueinander.
• On the density of discriminants of cyclic extensions of prime degree
• Advanced Topics in Computional Number Theory
• The Density of Abelian Cubic Fields
• Number Theory

This page was built for publication: Counting cubic extensions with given quadratic resolvent