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Mathematics of Computation

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A targeted Martinet search


Authors: Eric D. Driver and John W. Jones
Journal: Math. Comp. 78 (2009), 1109-1117
MSC (2000): Primary 11Y40; Secondary 11-04
DOI: https://doi.org/10.1090/S0025-5718-08-02178-9
Published electronically: August 22, 2008
MathSciNet review: 2476573
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Abstract: Constructing number fields with prescribed ramification is an important problem in computational number theory. In this paper, we consider the problem of computing all imprimitive number fields of a given degree which are unramified outside of a given finite set of primes $ S$ by combining the techniques of targeted Hunter searches with Martinet's relative version of Hunter's theorem. We then carry out this algorithm to generate complete tables of imprimitive number fields for degrees $ 4$ through $ 10$ and certain sets $ S$ of small primes.


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Additional Information

Eric D. Driver
Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804
Address at time of publication: Lockheed Martin Corporation, P.O. Box 85, Litchfield Park, Arizona 85340

John W. Jones
Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804

DOI: https://doi.org/10.1090/S0025-5718-08-02178-9
Received by editor(s): August 20, 2007
Received by editor(s) in revised form: May 13, 2008
Published electronically: August 22, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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