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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On simple families of cyclic polynomials


Author: Yuichi Rikuna
Journal: Proc. Amer. Math. Soc. 130 (2002), 2215-2218
MSC (2000): Primary 12F12; Secondary 11R20, 12E10
Published electronically: January 17, 2002
MathSciNet review: 1896400
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Abstract: We study polynomials giving cyclic extensions over rational function fields with one variable satisfying some conditions. By using them, we construct families of cyclic polynomials over some algebraic number fields. And these families give non-Kummer (or non-Artin-Schreier) cyclic extensions. In this paper, we see that our polynomials have two nice arithmetic properties. One is simplicity: our polynomials and their discriminants have more simple expressions than previous results, e.g. Dentzer (1995), Malle and Mazat (1999) and Smith (1991), etc. The other is a ``systematic'' property: if one of our polynomials $f$ gives an extension $L/K$, then for every intermediate field $M$we can easily find polynomials giving $M/K$ from $f$ systematically.


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Additional Information

Yuichi Rikuna
Affiliation: Department of Mathematical Sciences, School of Science and Engineering, Waseda University, 3–4–1 Ohkubo, Shinjuku-ku, Tokyo 169–8555, Japan
Email: rikuna@gm.math.waseda.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06414-6
PII: S 0002-9939(02)06414-6
Keywords: Inverse Galois problem, cyclic groups, cyclic polynomials
Received by editor(s): February 26, 2001
Published electronically: January 17, 2002
Additional Notes: The author is a Research Fellow of the Japan Society for the Promotion of Science, and this study was supported by Grant-in-Aid for JSPS Fellows
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2002 American Mathematical Society