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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computation of class numbers of quadratic number fields


Author: Stéphane Louboutin
Journal: Math. Comp. 71 (2002), 1735-1743
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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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.univ-mrs.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01367-9
PII: S 0025-5718(01)01367-9
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