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

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Analysis und Zahlentheorie (5010)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

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.

Originalsprache	englisch
Seiten (von - bis)	2197-2217
Seitenumfang	21
Fachzeitschrift	Journal of the London Mathematical Society
Jahrgang	107
Ausgabenummer	6
Frühes Online-Datum	20 Apr. 2023
DOIs	https://doi.org/10.1112/jlms.12737
Publikationsstatus	Veröffentlicht - Juni 2023

ASJC Scopus subject areas

Mathematik (insg.)

Fields of Expertise

Information, Communication & Computing

Zugriff auf Dokument

10.1112/jlms.12737Lizenz: CC BY 4.0

Journal of London Math Soc - 2023 - FreiEndgültige, publizierte Fassung, 229 KBLizenz: CC BY 4.0

Andere Dateien und Links

Verknüpfung zur Publikation in Scopus

Dieses zitieren

@article{5f5b53c6adea42f2a5a853eea5048fa7,

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 = jun,

doi = "10.1112/jlms.12737",

language = "English",

volume = "107",

pages = "2197--2217",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "Wiley",

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

Y1 - 2023/6

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.

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

ASJC Scopus subject areas

Fields of Expertise

Zugriff auf Dokument

Andere Dateien und Links

Fingerprint

Dieses zitieren