Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations
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- by Ki-ichiro Hashimoto and Akinari Hoshi PDF
- Math. Comp. 74 (2005), 1519-1530 Request permission
Abstract:
A general method of constructing families of cyclic polynomials over $\mathbb {Q}$ with more than one parameter will be discussed, which may be called a geometric generalization of the Gaussian period relations. Using this, we obtain explicit multi-parametric families of cyclic polynomials over $\mathbb {Q}$ of degree $3\le e\le 7$. We also give a simple family of cyclic polynomials with one parameter in each case, by specializing our parameters.References
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Additional Information
- Ki-ichiro Hashimoto
- Affiliation: Department of Mathematical Sciences, School of Science and Engineering, Waseda University, 3–4–1 Ohkubo, Shinjuku-ku, Tokyo 169–8555, Japan
- Email: khasimot@waseda.jp
- Akinari Hoshi
- Affiliation: Department of Mathematical Sciences, School of Science and Engineering, Waseda University, 3–4–1 Ohkubo, Shinjuku-ku, Tokyo 169–8555, Japan
- MR Author ID: 714371
- Email: hoshi@ruri.waseda.jp
- Received by editor(s): November 13, 2002
- Received by editor(s) in revised form: May 19, 2004
- Published electronically: February 14, 2005
- © Copyright 2005 American Mathematical Society
- Journal: Math. Comp. 74 (2005), 1519-1530
- MSC (2000): Primary 11R18, 11R27, 11T22, 12F10, 12F12
- DOI: https://doi.org/10.1090/S0025-5718-05-01750-3
- MathSciNet review: 2137015