We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.
@article{bwmeta1.element.doi-10_2478_s11533-013-0280-2,
author = {Ja Koo and Dong Shin},
title = {Completely normal elements in some finite abelian extensions},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1725-1731},
zbl = {1279.11106},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0280-2}
}
Ja Koo; Dong Shin. Completely normal elements in some finite abelian extensions. Open Mathematics, Tome 11 (2013) pp. 1725-1731. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0280-2/
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