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Number Fields with Discriminant ±2a3b and Galois Group An or Sn

Published online by Cambridge University Press:  01 February 2010

Gunter Malle  and
David P. Roberts
Gunter Malle
Affiliation:
Fachbereich Mathematik, TU Kaiserslautern, Erwin-Schrödinger-Strasse, D-67663 Kaiserslautern Germany, [email protected], http://www.mathematik.uni-kl.de/~malle/
David P. Roberts
Affiliation:
Division of Science and Mathematics, University of Minnesota-Morris, Morris, Minnesota, 56267, USA, [email protected], http://cda.morris.umn.edu/~roberts/

Abstract

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The authors present three-point and four-point covers having bad reduction at 2 and 3 only, with Galois group An or Sn for n equal to 9, 10, 12, 18, 28, and 33. By specializing these covers, they obtain number fields ramified at 2 and 3 only, with Galois group An or Sn for n equal to 9, 10, 11, 12, 17, 18, 25, 28, 30, and 33.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 8 , 2005 , pp. 80 - 101
Copyright
Copyright © London Mathematical Society 2005

References

1.Birch, B., ‘Noncongruence subgroups, covers and drawings’, The Grothendieck theory of dessins d'enfants, London Math. Soc. Lecture Note Ser. 200 (ed. Schneps, L., Cambridge Univ. Press, 1994) 25–46.CrossRefGoogle Scholar
2.Jones, J. W., Ongoing computer searches for number fields; updated results periodically posted at http://math.la.asu.edu/~jj/numberfields/.Google Scholar
3.Jones, J. W. and Roberts, D. P., ‘Sextic number fields with discriminant —j2a3b’, Number Theory (Ottawa, 1996), CRM Proc. Lecture Notes 19 (ed. Gupta, R. and Williams, K., Amer. Math. Soc, Providence, RI, 1999) 141–172.Google Scholar
4.Jones, J. W. and Roberts, D. P., ‘Septic number fields with discriminant ±2a 3b’, Math. Comp. 72 (2003) 244, 1975–1985.CrossRefGoogle Scholar
5.Katz, N. M., Rigid local systems, Ann. of Math. Stud. 139 (Princeton Univ. Press, Princeton, NJ, 1996).Google Scholar
6.Kraft, H., ‘A result of Hermite and equations of degree 5 and 6’, preprint, http://xxx.lanl.gov/abs/math.AC/0403323+.Google Scholar
7.Malle, G., ‘Fields of definition of some three-point ramified field extensions’, The Grothendieck theory of dessins d'enfants, London Math Soc Lecture Note Series 200 (ed. Schneps, L., Cambridge Univ. Press, 1994) 147–168.CrossRefGoogle Scholar
8.Malle, G. and Matzat, B. H., Inverse Galois theory, Monogr. Math. (Springer, Berlin, 1999).Google Scholar
9. PARI/GP, Version 2.1.5, Bordeaux, 2004, http://pari.math.u-bordeaux.fr/.Google Scholar
10.Roberts, D. P., ‘An ABC construction of number fields’, Number Theory (Montréal, 2002), CRM Proc. Lecture Notes 36 (ed. Kisilevsky, H. and Goren, E. Z., Amer. Math. Soc, Providence, RI, 2004) 237–267.Google Scholar