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
Number of pages	21
Journal	Journal of the London Mathematical Society
Early online date	20 Apr 2023
DOIs	https://doi.org/10.1112/jlms.12737
Publication status	E-pub ahead of print - 20 Apr 2023

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10.1112/jlms.12737Licence: CC BY

https://arxiv.org/abs/2209.10659

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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 (Formula presented.) of the time.",

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

note = "We thank Alex Bartel for useful discussions on genus groups and Hendrik Lenstra for askingthe question that led to Theorem1.5. We thank the anonymous referee for their careful readingof our paper. Christopher Frei was supported by EPSRC Grant EP/T01170X/1 and EP/T01170X/2.DanielLoughranwassupportedbyUKRIFutureLeadersFellowshipMR/V021362/1.RachelNew-ton was supported by EPSRC Grant EP/S004696/1 and EP/S004696/2, and UKRI Future LeadersFellowship MR/T041609/1 and MR/T041609/2",

year = "2023",

month = apr,

day = "20",

doi = "10.1112/jlms.12737",

language = "English",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "Oxford University Press",

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T1 - Distribution of genus numbers of abelian number fields

AU - Frei, Christopher

AU - Loughran, Daniel

AU - Newton, Rachel

N1 - We thank Alex Bartel for useful discussions on genus groups and Hendrik Lenstra for askingthe question that led to Theorem1.5. We thank the anonymous referee for their careful readingof our paper. Christopher Frei was supported by EPSRC Grant EP/T01170X/1 and EP/T01170X/2.DanielLoughranwassupportedbyUKRIFutureLeadersFellowshipMR/V021362/1.RachelNew-ton was supported by EPSRC Grant EP/S004696/1 and EP/S004696/2, and UKRI Future LeadersFellowship MR/T041609/1 and MR/T041609/2

PY - 2023/4/20

Y1 - 2023/4/20

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.

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U2 - 10.1112/jlms.12737

DO - 10.1112/jlms.12737

M3 - Article

SN - 0024-6107

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

ER -

Distribution of genus numbers of abelian number fields

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Fellowship FLF Geometric Analytic Number Theory

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Distribution of genus numbers of abelian number fields

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Fellowship FLF Geometric Analytic Number Theory

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