Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Tables of unit groups and class groups of quintic fields and a regulator bound

Author(s): M. Pohst; K. Wildanger.
Journal: Math. Comp. 67 (1998), 361-367.
MSC (1991): Primary 11Y40; Secondary 11R27, 11R29
MathSciNet review: 1451326
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Abstract: Using a new regulator bound we determine unit groups and class groups of the 289040 quintic algebraic number fields with absolute discriminant less than $2 \times 10^7$ (totally real fields), respectively $5 \times 10^6$ (other signatures). We list significant data.

References:

1.: H. Cohen, A Course in Computational Algebraic Number Theory, Springer, 1993. MR 94i:11105
2.: M. Daberkow, C. Fieker, J. Klüners, M. Pohst, K. Roegner, M. Schörnig and K. Wildanger, KANT V4, to appear in J. Symbolic Comp.
3.: M. Pohst, Computational Algebraic Number Theory, DMV Seminar 21, Birkhäuser, Basel 1993. MR 94j:11132
4.: M. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge Univ. Press, Cambridge 1989. MR 92b:11074
5.: A. Schwarz, M. Pohst and F. Diaz y Diaz, A Table of Quintic Number Fields, Math. Comp. 63 (1994), 361-376. MR 94i:11108

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