Distribution of genus numbers of abelian number fields

Christopher Frei; Daniel Loughran; Rachel Newton

Distribution of genus numbers of abelian number fields

Christopher Frei^*, Daniel Loughran, Rachel Newton

^*Corresponding author for this work

Mathematics

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

51 Downloads (Pure)

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
Journal	JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Publication status	Accepted/In press - 21 Feb 2023

Access to Document

GenusAccepted author manuscript, 503 KB

1 Finished
1 Active

Diophantine equations and local-global principles: into the wild
Newton, R. (Primary Investigator)
MRC Medical Research Council
1/08/2021 → 30/06/2025
Project: Research
Local-global principles: arithmetic statistics and obstructions
Newton, R. (Primary Investigator)
EPSRC Engineering and Physical Sciences Research Council
1/08/2021 → 30/09/2022
Project: Research

Cite this

@article{54ee4a04fc8a49298b5874be91791d8c,

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",

month = feb,

day = "21",

language = "English",

journal = "JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES",

issn = "0024-6107",

publisher = "Oxford University Press",

}

TY - JOUR

T1 - Distribution of genus numbers of abelian number fields

AU - Frei, Christopher

AU - Loughran, Daniel

AU - Newton, Rachel

PY - 2023/2/21

Y1 - 2023/2/21

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 0% 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 0% of the time.

M3 - Article

SN - 0024-6107

JO - JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

JF - JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

ER -

Distribution of genus numbers of abelian number fields

Abstract

Access to Document

Fingerprint

Projects

Diophantine equations and local-global principles: into the wild

Local-global principles: arithmetic statistics and obstructions

Cite this