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Mathematics of Computation

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Computation of relative class numbers
of CM-fields

Author: Stéphane Louboutin
Journal: Math. Comp. 66 (1997), 1185-1194
MSC (1991): Primary 11R29, 11Y35; Secondary 11R42
MathSciNet review: 1422790
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [Lou 1] S. Louboutin, Calcul des nombres de classes relatifs: application aux corps octiques quaternioniques à multiplication complexe, C. R. Acad. Sci. Paris 317 (1993), 643-646. MR 94j:11111
  • [Lou 2] 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
  • [Lou-Oka] S. Louboutin and R. Okazaki, The class number one problem for some non-abelian normal CM-fields of $2$-power degrees, preprint Univ. Caen 1996, to be submitted.
  • [LOO] 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 $L$-functions over real quadratic fields, J. Math. Kyoto Univ. 31 (1991), 1125-1153. MR 93b:11154
  • [Oka 2] R. Okazaki, An elementary proof for a theorem of Thomas and Vasquez, J. Nb. Th. 55 (1995), 197-208. MR 96m:11099
  • [Shin] 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
  • [Wa] L. C. Washington, Introduction to Cyclotomic Fields, Grad. Texts Math. 83, Springer-Verlag. MR 85g:11001

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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

Received by editor(s): December 5, 1995
Received by editor(s) in revised form: April 12, 1996
Article copyright: © Copyright 1997 American Mathematical Society

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