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

Allgemeine Mathematik

Fields of Expertise

Information, Communication & Computing

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10.1112/jlms.12737Lizenz: CC BY 4.0

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

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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.",

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Distribution of genus numbers of abelian number fields

Abstract

ASJC Scopus subject areas

Fields of Expertise

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