Dirichlet series associated to cubic fields with given quadratic resolvent

DOI10.1307/mmj/1401973050zbMath1305.11091arXiv1301.3563OpenAlexW2964335223MaRDI QIDQ2512534

Frank Thorne, Henri Cohen

Publication date: 7 August 2014

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.3563

zbMATH Keywords

Dirichlet seriesclass group\(S_3\)-sextic fields

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Algebraic number theory computations (11Y40) Class field theory (11R37) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29)

Related Items (9)

Identities for field extensions generalizing the Ohno–Nakagawa relations ⋮ Idélic approach in enumerating Heisenberg extensions ⋮ Counting 3-dimensional algebraic tori over \(\mathbb{Q}\) ⋮ Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves ⋮ On the p‐adic Stark conjecture at s=1 and applications ⋮ On the Ohno-Nakagawa theorem ⋮ Shintani’s zeta function is not a finite sum of Euler products ⋮ Dirichlet series associated to quartic fields with given cubic resolvent ⋮ Exact counting of $D_\ell $ number fields with given quadratic resolvent

Cites Work

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• Counting discriminants of number fields
• Density of cubic field discriminants
• DISCRIMINANTS CUBIQUES ET PROGRESSIONS ARITHMÉTIQUES
• A fast algorithm to compute cubic fields
• A conjecture on coincidence among the zeta functions associated with the space of binary cubic forms
• Mass Formulae for Extensions of Local Fields, and Conjectures on the Density of Number Field Discriminants

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