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Title: A determinant formula for the relative class number of an imaginary abelian number field (English)
Author: Hirabayashi, Mikihito
Language: English
Journal: Communications in Mathematics
ISSN: 1804-1388
Volume: 22
Issue: 2
Year: 2014
Pages: 133-140
Summary lang: English
Category: math
Summary: We give a new formula for the relative class number of an imaginary abelian number field $K$ by means of determinant with elements being integers of a cyclotomic field generated by the values of an odd Dirichlet character associated to $K$. We prove it by a specialization of determinant formula of Hasse. (English)
Keyword: imaginary abelian number field
Keyword: relative class number
Keyword: determinant
Keyword: class number formula
MSC: 11R20
MSC: 11R29
idZBL: Zbl 06410230
idMR: MR3303134
Date available: 2015-01-27T09:37:01Z
Last updated: 2020-01-05
Stable URL:
Reference: [1] Girstmair, K.: The relative class numbers of imaginary cyclic fields of degrees 4, 6, 8 and 10.Math. Comp., 61, 1993, 881-887, Zbl 0787.11046, MR 1195428
Reference: [2] Hasse, H.: Über die Klassenzahl abelscher Zahlkörper.1952, Akademie-Verlag, Berlin, Reprinted with an introduction by J. Martinet, Springer Verlag, Berlin (1985). Zbl 0046.26003, MR 0842666
Reference: [3] Hirabayashi, M., Yoshino, K.: Remarks on unit indices of imaginary abelian number fields.Manuscripta math., 60, 1988, 423-436, Zbl 0654.12002, MR 0933473, 10.1007/BF01258662
Reference: [4] Washington, L.C.: Introduction to Cyclotomic Fields, 2nd edition.1997, Springer Verlag, Berlin, MR 1421575
Reference: [5] Yamamura, K.: Bibliography on determinantal expressions of relative class numbers of imaginary abelian number fields.Number Theory. Dreaming in Dreams. Proceedings of the 5th China-Japan Seminar, 2010, 244-250, World Sci. Publ., Hackensack, Zbl 1202.11001, MR 2798466


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