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 | 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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Computation of and of relative class numbers of CM-fields.*Nagoya Math. J.***161**(2001), 171-191. CMP**2001:09****[MoWi]**R. A. Mollin and H. C. Williams,*Computation of the class number of a real quadratic field*, Utilitas Math.**41**(1992), 259–308. MR**1162532****[ScWa]**René Schoof and Lawrence C. Washington,*Quintic polynomials and real cyclotomic fields with large class numbers*, Math. Comp.**50**(1988), no. 182, 543–556. MR**929552**, 10.1090/S0025-5718-1988-0929552-2**[StWi]**A. J. Stephens and H. C. Williams,*Computation of real quadratic fields with class number one*, Math. Comp.**51**(1988), no. 184, 809–824. MR**958644**, 10.1090/S0025-5718-1988-0958644-7**[WiBr]**H. C. Williams and J. Broere,*A computational technique for evaluating 𝐿(1,𝜒) and the class number of a real quadratic field*, Math. Comp.**30**(1976), no. 136, 887–893. MR**0414522**, 10.1090/S0025-5718-1976-0414522-5

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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

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