On the ideal class group on which the alternating group of degree five acts and special values of Artin \(L\)-functions

DOI10.1007/s11139-021-00540-6zbMath1503.11139OpenAlexW4220988884MaRDI QIDQ2168694

Yutaka Konomi

Publication date: 26 August 2022

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-021-00540-6

zbMATH Keywords

\(L\)-functionsalternating groupsclass groups

Mathematics Subject Classification ID

Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42) Iwasawa theory (11R23) Simple groups: alternating groups and groups of Lie type (20D06)

Cites Work

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• The ideal class groups of dihedral extensions over imaginary quadratic fields and the special values of the Artin \(L\)-function
• Values of abelian \(L\)-functions at negative integers over totally real fields
• On the \(p\)-rank of the ideal class group of a normal extension with simple Galois group
• On the special values of Artin \(L\)-functions for dihedral extensions
• On a conjecture of Brumer
• On Brumer's family of RM-curves of genus two

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