Computation of class numbers of quadratic number fields
Author:
Stéphane Louboutin
Journal:
Math. Comp. 71 (2002), 17351743
MSC (2000):
Primary 11R11, 11R29, 11R21, 11Y35
Published electronically:
November 21, 2001
MathSciNet review:
1933052
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Abstract: We explain how one can dispense with the numerical computation of approximations to the transcendental integral functions involved when computing class numbers of quadratic number fields. We therefore end up with a simpler and faster method for computing class numbers of quadratic number fields. We also explain how to end up with a simpler and faster method for computing relative class numbers of imaginary abelian number fields.
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Computation of relative class numbers of CMfields by using Hecke functions. Math. Comp. 69 (2000), 371393. MR 2000i:11172
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 S. Louboutin.
Computation of and of relative class numbers of CMfields. Nagoya Math. J. 161 (2001), 171191. CMP 2001:09
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 R. A. Mollin and H. C. Williams.
Computation of the class number of a real quadratic field. Utilitas Math. 41 (1992), 259308. MR 93d:11134
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 R. Schoof and L. C. Washington.
Quintic polynomials and real cyclotomic fields with large class numbers. Math. Comp. 50 (1988), 543556. MR 89h:11067b
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Additional Information
Stéphane Louboutin
Affiliation:
Institut de Mathématiques de Luminy, UPR 906, 163, avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France
Email:
loubouti@iml.univmrs.fr
DOI:
http://dx.doi.org/10.1090/S0025571801013679
PII:
S 00255718(01)013679
Keywords:
Quadratic number field,
class number,
Dirichlet $L$function,
relative class number.
Received by editor(s):
March 29, 2000
Received by editor(s) in revised form:
November 27, 2000
Published electronically:
November 21, 2001
Article copyright:
© Copyright 2001
American Mathematical Society
