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Mathematics of Computation

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Number fields with solvable Galois groups and small Galois root discriminants


Authors: John W. Jones and Rachel Wallington
Journal: Math. Comp. 81 (2012), 555-567
MSC (2010): Primary 11R21; Secondary 11R37
DOI: https://doi.org/10.1090/S0025-5718-2011-02511-1
Published electronically: June 3, 2011
MathSciNet review: 2833508
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Abstract: We apply class field theory to compute complete tables of number fields with Galois root discriminant less than $ 8\pi e^{\gamma}$. This includes all solvable Galois groups which appear in degree less than $ 10$, groups of order less than $ 24$, and all dihedral groups $ D_p$ where $ p$ is prime.


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Additional Information

John W. Jones
Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, P.O. Box 871804, Tempe, Arizona 85287
Email: jj@asu.edu

Rachel Wallington
Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, P.O. Box 871804, Tempe, Arizona 85287
Address at time of publication: Faith Christian School, P.O. Box 31300, Mesa, Arizona 85275
Email: rwallington@faith-christian.org

DOI: https://doi.org/10.1090/S0025-5718-2011-02511-1
Received by editor(s): July 24, 2010
Received by editor(s) in revised form: December 15, 2010
Published electronically: June 3, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.