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

DOI:
https://doi.org/10.1090/S0025-5718-01-01367-9

Published electronically:
November 21, 2001

MathSciNet review:
1933052

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-01-01367-9

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