On simple families of cyclic polynomials
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- by Yūichi Rikuna PDF
- Proc. Amer. Math. Soc. 130 (2002), 2215-2218 Request permission
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.References
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Additional Information
- Yūichi 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
- 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
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1896400