Distribution of genus numbers of abelian number fields-Reference-Cited by-同舟云学术

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Distribution of genus numbers of abelian number fields

Published:2023-04-20 Issue:6 Volume:107 Page:2197-2217
ISSN:0024-6107
Container-title:Journal of the London Mathematical Society
language:en
Short-container-title:Journal of London Math Soc

Author:

Frei Christopher¹,Loughran Daniel²,Newton Rachel³

Affiliation:

1. TU Graz Institute of Analysis and Number Theory Graz Austria

2. Department of Mathematical Sciences University of Bath, Claverton Down Bath UK

3. Department of Mathematics King's College London, Strand London UK

Abstract

AbstractWe study the quantitative behaviour of genus numbers of abelian extensions of number fields with given Galois group. We prove an asymptotic formula for the average value of the genus number and show that any given genus number appears only of the time.

Funder

Engineering and Physical Sciences Research Council

Publisher

Wiley

Subject

General Mathematics

Link

https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/jlms.12737

Reference20 articles.

1. Heuristics on class groups of number fields

2. Density of discriminants of cubic extensions;Datskovsky B.;J. Reine Angew. Math.,1988

3. On the density of discriminants of cubic fields. II

4. On ℓ-torsion in class groups of number fields

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