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

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

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 0% 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 - Jun 2023

ASJC Scopus subject areas

General Mathematics

Fields of Expertise

Information, Communication & Computing

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10.1112/jlms.12737Licence: CC BY 4.0

Journal of London Math Soc - 2023 - FreiFinal published version, 229 KBLicence: CC BY 4.0

Cite this

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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 0% of the time.",

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

year = "2023",

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doi = "10.1112/jlms.12737",

language = "English",

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AU - Newton, Rachel

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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 0% of the time.

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DO - 10.1112/jlms.12737

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JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

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Distribution of genus numbers of abelian number fields

Abstract

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