Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics

Blair K. Spearman[1]; Kenneth S. Williams[2]

  • [1] Department of Mathematics and Statistics Okanagan University College Kelowna, B.C. Canada V1V 1V7
  • [2] School of Mathematics and Statistics Carleton University Ottawa, Ontario, Canada K1S 5B6

Journal de Théorie des Nombres de Bordeaux (2004)

  • Volume: 16, Issue: 1, page 215-220
  • ISSN: 1246-7405

Abstract

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Explicit normal integral bases are given for some cyclic quintic fields defined by Emma Lehmer’s parametric family of quintics.

How to cite

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Spearman, Blair K., and Williams, Kenneth S.. "Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics." Journal de Théorie des Nombres de Bordeaux 16.1 (2004): 215-220. <http://eudml.org/doc/249269>.

@article{Spearman2004,
abstract = {Explicit normal integral bases are given for some cyclic quintic fields defined by Emma Lehmer’s parametric family of quintics.},
affiliation = {Department of Mathematics and Statistics Okanagan University College Kelowna, B.C. Canada V1V 1V7; School of Mathematics and Statistics Carleton University Ottawa, Ontario, Canada K1S 5B6},
author = {Spearman, Blair K., Williams, Kenneth S.},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {normal integral basis; Lehmer family of quintic fields},
language = {eng},
number = {1},
pages = {215-220},
publisher = {Université Bordeaux 1},
title = {Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics},
url = {http://eudml.org/doc/249269},
volume = {16},
year = {2004},
}

TY - JOUR
AU - Spearman, Blair K.
AU - Williams, Kenneth S.
TI - Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2004
PB - Université Bordeaux 1
VL - 16
IS - 1
SP - 215
EP - 220
AB - Explicit normal integral bases are given for some cyclic quintic fields defined by Emma Lehmer’s parametric family of quintics.
LA - eng
KW - normal integral basis; Lehmer family of quintic fields
UR - http://eudml.org/doc/249269
ER -

References

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  1. V. Acciaro and C. Fieker, Finding normal integral bases of cyclic number fields of prime degree. J. Symbolic Comput. 30 (2000), 239–252. Zbl0977.11047MR1777167
  2. I. Gaál and M. Pohst, Power integral bases in a parametric family of totally real cyclic quintics. Math. Comp. 66 (1997), 1689–1696. Zbl0899.11064MR1423074
  3. S. Jeannin, Nombre de classes et unités des corps de nombres cycliques quintiques d’ E. Lehmer. J. Théor. Nombres Bordeaux 8 (1996), 75–92. Zbl0865.11070MR1399947
  4. E. Lehmer, Connection between Gaussian periods and cyclic units. Math. Comp. 50 (1988), 535–541. Zbl0652.12004MR929551
  5. W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers. Springer - Verlag, Berlin 1990. Zbl1159.11039MR1055830
  6. R. Schoof and L. C. Washington, Quintic polynomials and real cyclotomic fields with large class numbers. Math. Comp. 50 (1988), 543–556. Zbl0649.12007MR929552
  7. B. K. Spearman and K. S. Williams, The discriminant of a cyclic field of odd prime degree. Rocky Mountain J. Math. To appear. Zbl1074.11059MR2038542

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