Explicit normal integral bases are given for some cyclic quintic fields defined by Emma Lehmer’s parametric family of quintics.
Nous donnons des bases normales entières explicites pour des extensions cycliques quintiques définies par la famille paramétrée de quintiques d’Emma Lehmer.
Blair K. Spearman 1; Kenneth S. Williams 2
@article{JTNB_2004__16_1_215_0, author = {Blair K. Spearman and Kenneth S. Williams}, title = {Normal integral bases for {Emma} {Lehmer{\textquoteright}s} parametric family of cyclic quintics}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {215--220}, publisher = {Universit\'e Bordeaux 1}, volume = {16}, number = {1}, year = {2004}, doi = {10.5802/jtnb.443}, mrnumber = {2145582}, zbl = {02184641}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.443/} }
TY - JOUR AU - Blair K. Spearman AU - Kenneth S. Williams TI - Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics JO - Journal de théorie des nombres de Bordeaux PY - 2004 SP - 215 EP - 220 VL - 16 IS - 1 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.443/ DO - 10.5802/jtnb.443 LA - en ID - JTNB_2004__16_1_215_0 ER -
%0 Journal Article %A Blair K. Spearman %A Kenneth S. Williams %T Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics %J Journal de théorie des nombres de Bordeaux %D 2004 %P 215-220 %V 16 %N 1 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.443/ %R 10.5802/jtnb.443 %G en %F JTNB_2004__16_1_215_0
Blair K. Spearman; Kenneth S. Williams. Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics. Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 1, pp. 215-220. doi : 10.5802/jtnb.443. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.443/
[1] V. Acciaro and C. Fieker, Finding normal integral bases of cyclic number fields of prime degree. J. Symbolic Comput. 30 (2000), 239–252. | MR | Zbl
[2] I. Gaál and M. Pohst, Power integral bases in a parametric family of totally real cyclic quintics. Math. Comp. 66 (1997), 1689–1696. | MR | Zbl
[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. | Numdam | MR | Zbl
[4] E. Lehmer, Connection between Gaussian periods and cyclic units. Math. Comp. 50 (1988), 535–541. | MR | Zbl
[5] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers. Springer - Verlag, Berlin 1990. | MR | Zbl
[6] R. Schoof and L. C. Washington, Quintic polynomials and real cyclotomic fields with large class numbers. Math. Comp. 50 (1988), 543–556. | MR | Zbl
[7] B. K. Spearman and K. S. Williams, The discriminant of a cyclic field of odd prime degree. Rocky Mountain J. Math. To appear. | MR | Zbl
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