Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
Full-text PDF Free Access

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] Stéphane Louboutin, Calcul des nombres de classes relatifs: application aux corps octiques quaternioniques à multiplication complexe, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 7, 643–646 (French, with English and French summaries). MR 1245090
  • [Lou 2] Stéphane Louboutin, Calcul des nombres de classes relatifs de certains corps de classes de Hilbert, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), no. 4, 321–325 (French, with English and French summaries). MR 1289305
  • [Lou 3] Stéphane Louboutin, Calcul du nombre de classes des corps de nombres, Pacific J. Math. 171 (1995), no. 2, 455–467 (French, with French summary). MR 1372239
  • [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] Ryotaro Okazaki, On evaluation of 𝐿-functions over real quadratic fields, J. Math. Kyoto Univ. 31 (1991), no. 4, 1125–1153. MR 1141089
  • [Oka 2] Ryotaro Okazaki, An elementary proof for a theorem of Thomas and Vasquez, J. Number Theory 55 (1995), no. 2, 197–208. MR 1366570,
  • [Shin] Takuro Shintani, On evaluation of zeta functions of totally real algebraic number fields at non-positive integers, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), no. 2, 393–417. MR 0427231
  • [Wa] Lawrence C. Washington, Introduction to cyclotomic fields, Graduate Texts in Mathematics, vol. 83, Springer-Verlag, New York, 1982. MR 718674

Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 11R29, 11Y35, 11R42

Retrieve articles in all journals with MSC (1991): 11R29, 11Y35, 11R42

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