Distribution of genus numbers of abelian number fields

Christopher Frei; Daniel Loughran; Rachel Newton

doi:10.1112/jlms.12737

Distribution of genus numbers of abelian number fields

Christopher Frei, Daniel Loughran, Rachel Newton

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We 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 (Formula presented.) of the time.

Original language	English
Pages (from-to)	2197-2217
Number of pages	21
Journal	Journal of the London Mathematical Society
Volume	107
Issue number	6
Early online date	20 Apr 2023
DOIs	https://doi.org/10.1112/jlms.12737
Publication status	Published - 1 Jun 2023

Funding

We thank Alex Bartel for useful discussions on genus groups and Hendrik Lenstra for asking the question that led to Theorem 1.5 . We thank the anonymous referee for their careful reading of our paper. Christopher Frei was supported by EPSRC Grant EP/T01170X/1 and EP/T01170X/2. Daniel Loughran was supported by UKRI Future Leaders Fellowship MR/V021362/1. Rachel Newton was supported by EPSRC Grant EP/S004696/1 and EP/S004696/2, and UKRI Future Leaders Fellowship MR/T041609/1 and MR/T041609/2.

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/T01170X/1, EP/T01170X/2, EP/S004696/1, EP/S004696/2

Access to Document

10.1112/jlms.12737Licence: CC BY

https://arxiv.org/abs/2209.10659

Cite this

@article{932eadee3e074331a1190f64468c430d,

title = "Distribution of genus numbers of abelian number fields",

abstract = "We 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 (Formula presented.) of the time.",

author = "Christopher Frei and Daniel Loughran and Rachel Newton",

year = "2023",

month = jun,

day = "1",

doi = "10.1112/jlms.12737",

language = "English",

volume = "107",

pages = "2197--2217",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "John Wiley and Sons Inc.",

number = "6",

}

TY - JOUR

T1 - Distribution of genus numbers of abelian number fields

AU - Frei, Christopher

AU - Loughran, Daniel

AU - Newton, Rachel

PY - 2023/6/1

Y1 - 2023/6/1

N2 - We 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 (Formula presented.) of the time.

AB - We 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 (Formula presented.) of the time.

UR - http://www.scopus.com/inward/record.url?scp=85153355468&partnerID=8YFLogxK

U2 - 10.1112/jlms.12737

DO - 10.1112/jlms.12737

M3 - Article

SN - 0024-6107

VL - 107

SP - 2197

EP - 2217

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 6

ER -

Distribution of genus numbers of abelian number fields

Abstract

Funding

Access to Document

Other files and links

Fingerprint

Fellowship FLF Geometric Analytic Number Theory

Cite this

Distribution of genus numbers of abelian number fields

Abstract

Funding

Access to Document

Other files and links

Fingerprint

Projects

Fellowship FLF Geometric Analytic Number Theory

Cite this