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

DOI:
https://doi.org/10.1090/S0002-9939-02-06414-6

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 gives an extension , then for every intermediate field we can easily find polynomials giving from 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:
https://doi.org/10.1090/S0002-9939-02-06414-6

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