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Computation of relative class numbers of CM-fields

Author(s): Stéphane Louboutin.
Journal: Math. Comp. 66 (1997), 1185-1194.
MSC (1991): Primary 11R29, 11Y35; Secondary 11R42
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Abstract: It was well known that it is easy to compute relative class numbers of abelian CM-fields by using generalized Bernoulli numbers (see Theorem 4.17 in Introduction to cyclotomic fields by L. C. Washington, Grad. Texts in Math., vol. 83, Springer-Verlag, 1982). Here, we provide a technique for computing the relative class number of any CM-field.

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Additional Information:

Stéphane Louboutin
Affiliation: Université de Caen, U.F.R. Sciences, Département de Mathématiques, Esplanade de la Paix, 14032 Caen Cedex, France
Email: loubouti@math.unicaen.fr

DOI: 10.1090/S0025-5718-97-00863-6
PII: S 0025-5718(97)00863-6
Received by editor(s): December 5, 1995
Received by editor(s) in revised form: April 12, 1996
Copyright of article: Copyright 1997, American Mathematical Society

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The following works have cited this article

Yang H.-S. and Kwon S.-H., The non-normal quartic CM-fields and the octic dihedral CM-fields with relative class number two, J. Number Theory 79 (1999), 175-193. (English)

Louboutin S., Computation of relative class numbers of CM-fields by using Hecke $L$-functions, Math. Comp. 69 (2000), 371-393. (English)

S. Louboutin, Computation of $L(0,\chi )$ and of relative class numbers of CM-fields, Nagoya Math. J. 161 (2001), 171-191. (English)

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