On Unramified Galois Extensions of Certain Algebraic Number Fields

KOMATSU, Kenzo; NODERA, Takashi

Tokyo J. of Math., Tome 16 (1993) no. 2, p. 351-354 / Harvested from Project Euclid

Résumé

Let $a\in\mathbf{Z}$ such that $a\neq 1$, $a\neq-2^{17}$ and $(17,a)=1$. Let $\alpha_1,\alpha_2,\ldots,\alpha_{17}$ denote the roots of $x^{17}+ax+a=0$. It is shown that every prime ideal is unramified in $\mathbf{Q}(\alpha_1,\alpha_2,\ldots,\alpha_{17})/\mathbf{Q}(\alpha_1)$ if and only if $a=2^{62}n^2+4605612312119580521n+1149886651258880054$ for some $n\in\mathbf{Z}$.

Publié le : 1993-12-15
Classification:

@article{1270128489,
     author = {KOMATSU, Kenzo and NODERA, Takashi},
     title = {On Unramified Galois Extensions of Certain Algebraic Number Fields},
     journal = {Tokyo J. of Math.},
     volume = {16},
     number = {2},
     year = {1993},
     pages = { 351-354},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1270128489}
}

KOMATSU, Kenzo; NODERA, Takashi. On Unramified Galois Extensions of Certain Algebraic Number Fields. Tokyo J. of Math., Tome 16 (1993) no. 2, pp.  351-354. http://gdmltest.u-ga.fr/item/1270128489/