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

 

Computing the Hilbert class field
of real quadratic fields


Authors: Henri Cohen and Xavier-François Roblot
Journal: Math. Comp. 69 (2000), 1229-1244
MSC (1991): Primary 11R37, 11R42; Secondary 11Y35
Published electronically: March 10, 1999
MathSciNet review: 1651747
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Abstract | References | Similar Articles | Additional Information

Abstract: Using the units appearing in Stark's conjectures on the values of $L$-functions at $s=0$, we give a complete algorithm for computing an explicit generator of the Hilbert class field of a real quadratic field.


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Additional Information

Henri Cohen
Affiliation: Laboratoire A2X, Université Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France
Email: cohen@math.u-bordeaux.fr

Xavier-François Roblot
Affiliation: Laboratoire A2X, Université Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France
Address at time of publication: Department of Computer Science, Concordia University, 1455 de Maisonneuve Blvd West, Montreal, Quebec, H3G 1M8
Email: roblot@cs.concordia.ca

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01111-4
PII: S 0025-5718(99)01111-4
Received by editor(s): January 19, 1998
Received by editor(s) in revised form: September 10, 1998
Published electronically: March 10, 1999
Article copyright: © Copyright 2000 American Mathematical Society