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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
MathSciNet review:
1422790
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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.
References:
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- S. Louboutin, Calcul des nombres de classes relatifs de certains corps de classes de Hilbert, C. R. Acad. Sci. Paris. 319 (1994), 321-325. MR 95g:11111
- [Lou 3]
- S. Louboutin, Calcul du nombre de classes des corps de nombres, Pacific J. Math. 171 (1995), 455-467. MR 97a:11176
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- S. Louboutin and R. Okazaki, The class number one problem for some non-abelian normal CM-fields of
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- S. Louboutin, R. Okazaki and M. Olivier, The class number one problem for some non-abelian normal CM-fields, to appear in Trans. Amer. Math. Soc. CMP 96:12
- [Oka 1]
- R. Okazaki, On evaluation of
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- R. Okazaki, An elementary proof for a theorem of Thomas and Vasquez, J. Nb. Th. 55 (1995), 197-208. MR 96m:11099
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- T. Shintani, On evaluation of zeta functions of totally real algebraic number fields at non-positive integers, J. Fac. Sci. Univ. Tokyo 23 (1976), 393-417. MR 55:266
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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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