Dirichlet series associated to quartic fields with given cubic resolvent

DOI10.1007/s40993-015-0001-yzbMath1411.11099arXiv1302.5728OpenAlexW2247966472WikidataQ59468770 ScholiaQ59468770MaRDI QIDQ2520545

Frank Thorne, Henri Cohen

Publication date: 15 December 2016

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.5728

zbMATH Keywords

Dirichlet seriesquartic fieldscubic resolvent

Mathematics Subject Classification ID

Cubic and quartic extensions (11R16) Zeta functions and (L)-functions of number fields (11R42)

Related Items (5)

Octahedral extensions with a given cubic subfield ⋮ Computing septic number fields ⋮ Idélic approach in enumerating Heisenberg extensions ⋮ Counting 3-dimensional algebraic tori over \(\mathbb{Q}\) ⋮ Levels of distribution for sieve problems in prehomogeneous vector spaces

Uses Software

• PARI/GP

Cites Work

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• Counting cubic extensions with given quadratic resolvent
• Arithmetic of octahedral sextics
• Counting cyclic quartic extensions of a number field
• Prehomogeneous vector spaces and field extensions
• On the relations among the class numbers of binary cubic forms
• Higher composition laws. III: The parametrization of quartic rings
• Higher composition laws. II: On cubic analogues of Gauss composition
• A database of local fields
• The density of discriminants of quartic rings and fields
• Dirichlet series associated to cubic fields with given quadratic resolvent
• Counting discriminants of number fields
• Quartic fields with the symmetric group
• A database of number fields
• Identities for field extensions generalizing the Ohno–Nakagawa relations
• On the probabilities of local behaviors in abelian field extensions
• Distribution of Discriminants of Abelian Extensions
• On the density of discriminants of quartic fields.
• Über die Beziehung der Klassenzahlen quadratischer Körper zueinander.
• A conjecture on coincidence among the zeta functions associated with the space of binary cubic forms
• Classnumbers and unit signatures
• The Density of Abelian Cubic Fields
• Number theory. Transl. from the 3rd German edition, edited and with a preface by Horst Günter Zimmer.

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