Completely normal elements in some finite abelian extensions

Ja Koo; Dong Shin

Open Mathematics (2013)

  • Volume: 11, Issue: 10, page 1725-1731
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Ja Koo, and Dong Shin. "Completely normal elements in some finite abelian extensions." Open Mathematics 11.10 (2013): 1725-1731. <http://eudml.org/doc/269002>.

@article{JaKoo2013,
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.},
author = {Ja Koo, Dong Shin},
journal = {Open Mathematics},
keywords = {Cyclotomic extensions; Modular functions; Normal bases; cyclotomic extensions; modular functions; normal bases},
language = {eng},
number = {10},
pages = {1725-1731},
title = {Completely normal elements in some finite abelian extensions},
url = {http://eudml.org/doc/269002},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Ja Koo
AU - Dong Shin
TI - Completely normal elements in some finite abelian extensions
JO - Open Mathematics
PY - 2013
VL - 11
IS - 10
SP - 1725
EP - 1731
AB - 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.
LA - eng
KW - Cyclotomic extensions; Modular functions; Normal bases; cyclotomic extensions; modular functions; normal bases
UR - http://eudml.org/doc/269002
ER -

References

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  11. [11] Okada T., On an extension of a theorem of S. Chowla, Acta Arith., 1980/81, 38(4), 341–345 [WoS] 
  12. [12] Shimura G., Introduction to the Arithmetic Theory of Automorphic Functions, Publ. Math. Soc. Japan, 11, Iwanami Shoten/Princeton University Press, Tokyo/Princeton, 1971 Zbl0221.10029
  13. [13] van der Waerden B.L., Algebra I, Springer, New York, 1991 http://dx.doi.org/10.1007/978-1-4684-9999-5[Crossref] 
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