Distribution of genus numbers of abelian number fields

DOI10.1112/jlms.12737arXiv2209.10659OpenAlexW4366583914WikidataQ123015624 ScholiaQ123015624MaRDI QIDQ6176460

Daniel Loughran, Christopher Frei, Rachel Newton

Publication date: 23 August 2023

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.10659

zbMATH Keywords

Galois groupgenusabelian number fieldsFrobenius functions

Mathematics Subject Classification ID

Class field theory (11R37) Class numbers, class groups, discriminants (11R29) Density theorems (11R45) Analysis on specific locally compact and other abelian groups (43A70)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the genus field in algebraic number fields
• On \(\ell\)-torsion in class groups of number fields
• Number fields with prescribed norms (with an appendix by Yonatan Harpaz and Olivier Wittenberg)
• Average bounds for the \(\ell\)-torsion in class groups of cyclic extensions
• On the probabilities of local behaviors in abelian field extensions
• Central Extensions, Galois Groups, and Ideal Class Groups of Number Fields
• Density of discriminants of cubic extensions.
• Ideal-theoretic characterization of the relative genus field.
• The Hasse norm principle for abelian extensions
• Genus numbers of cyclic and dihedral extensions of prime degree
• The Genus Field and Genus Number in Algebraic Number Fields
• The genus field and genus group in finite number fields
• On the density of discriminants of cubic fields. II
• Counting quintic fields with genus number one

This page was built for publication: Distribution of genus numbers of abelian number fields