Abstract
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.
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Koo, J.K., Shin, D.H. Completely normal elements in some finite abelian extensions. centr.eur.j.math. 11, 1725–1731 (2013). https://doi.org/10.2478/s11533-013-0280-2
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DOI: https://doi.org/10.2478/s11533-013-0280-2