An algorithm to compute relative cubic fields
Author:
Anna Morra
Journal:
Math. Comp. 82 (2013), 2343-2361
MSC (2010):
Primary 11R16, 11Y40
DOI:
https://doi.org/10.1090/S0025-5718-2013-02686-5
Published electronically:
March 14, 2013
MathSciNet review:
3073205
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let be an imaginary quadratic number field with class number
. We describe a new, essentially linear-time algorithm, to list all isomorphism classes of cubic extensions
up to a bound
on the norm of the relative discriminant ideal. The main tools are Taniguchi's [18] generalization of Davenport-Heilbronn parametrisation of cubic extensions, and reduction theory for binary cubic forms over imaginary quadratic fields. Finally, we give numerical data for
, and we compare our results with ray class field algorithm results, and with asymptotic heuristics, based on a generalization of Roberts' conjecture [19].
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Additional Information
Anna Morra
Affiliation:
Université Rennes 1, IRMAR, 263 avenue du Général Leclerc, CS74205, 35042 Rennes Cedex, France
DOI:
https://doi.org/10.1090/S0025-5718-2013-02686-5
Received by editor(s):
March 21, 2011
Received by editor(s) in revised form:
August 26, 2011, and February 5, 2012
Published electronically:
March 14, 2013
Article copyright:
© Copyright 2013
American Mathematical Society