Special units in real cyclic sextic fields
HTML articles powered by AMS MathViewer
- by Marie-Nicole Gras PDF
- Math. Comp. 48 (1987), 179-182 Request permission
Abstract:
We study the real cyclic sextic fields generated by a root w of ${(X - 1)^6} - ({t^2} + 108){({X^2} + X)^2}$, $t \in {\mathbf {Z}} - \{ 0, \pm 6, \pm 26\}$ . We show that, when ${t^2} + 108$ is square-free (except for powers of 2 and 3), and $t \ne 0$, $\pm 10$, $\pm 54$, then w is a generator of the module of relative units. The details of the proofs are given in [3].References
- Gary Cornell and Lawrence C. Washington, Class numbers of cyclotomic fields, J. Number Theory 21 (1985), no. 3, 260–274. MR 814005, DOI 10.1016/0022-314X(85)90055-1
- Georges Gras and Marie-Nicole Gras, Calcul du nombre de classes et des unités des extensions abéliennes réelles de $Q$, Bull. Sci. Math. (2) 101 (1977), no. 2, 97–129 (French). MR 480423 M.-N. Gras, "Famillés d’unités dans les extensions cycliques réelles de degré 6 de Q," Publ. Math. Besançon, 1984/85-1985/86. M.-N. Gras, "Table numérique du nombre de classes et des unités des extensions cycliques réelles de degré 4 de Q," Publ. Math. Besançon, 1977/78, fasc. 2, pp. 1-26 & 1-53.
- Sirpa Mäki, The determination of units in real cyclic sextic fields, Lecture Notes in Mathematics, vol. 797, Springer, Berlin, 1980. MR 584794
- Eric Seah, Lawrence C. Washington, and Hugh C. Williams, The calculation of a large cubic class number with an application to real cyclotomic fields, Math. Comp. 41 (1983), no. 163, 303–305. MR 701641, DOI 10.1090/S0025-5718-1983-0701641-2
- Daniel Shanks, The simplest cubic fields, Math. Comp. 28 (1974), 1137–1152. MR 352049, DOI 10.1090/S0025-5718-1974-0352049-8
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Math. Comp. 48 (1987), 179-182
- MSC: Primary 11R27; Secondary 11R20
- DOI: https://doi.org/10.1090/S0025-5718-1987-0866107-1
- MathSciNet review: 866107