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Exact counting of $ D_\ell$ number fields with given quadratic resolvent

Author: Henri Cohen
Journal: Math. Comp. 84 (2015), 1933-1951
MSC (2010): Primary 11R16, 11R20, 11R29
Published electronically: January 12, 2015
MathSciNet review: 3335898
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Abstract: We give efficient numerical methods for counting exactly the number of $ D_\ell $ number fields of degree $ \ell $ with given quadratic resolvent, for calculating the constants occurring in their asymptotic expansions, and we give tables for typical cases.

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  • [1] Henri Cohen, Advanced Topics in Computational Number Theory, Graduate Texts in Mathematics, vol. 193, Springer-Verlag, New York, 2000. MR 1728313 (2000k:11144)
  • [2] Henri Cohen, Comptage exact de discriminants d'extensions abéliennes, J. Théor. Nombres Bordeaux 12 (2000), no. 2, 379-397 (French, with English and French summaries). Colloque International de Théorie des Nombres (Talence, 1999). MR 1823191 (2002b:11158)
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Additional Information

Henri Cohen
Affiliation: Université de Bordeaux, Institut de Mathématiques, U.M.R. 5251 du C.N.R.S., 351 Cours de la Libération, 33405 TALENCE Cedex, France

Received by editor(s): August 20, 2013
Received by editor(s) in revised form: November 17, 2013
Published electronically: January 12, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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