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Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations


Authors: Ki-ichiro Hashimoto and Akinari Hoshi
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
Published electronically: February 14, 2005
MathSciNet review: 2137015
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Abstract | References | Similar Articles | Additional Information

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.


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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
Email: hoshi@ruri.waseda.jp

DOI: https://doi.org/10.1090/S0025-5718-05-01750-3
Keywords: Inverse Galois theory, generic polynomials, cyclic polynomials, Gaussian periods, Jacobi sums, cyclotomic numbers.
Received by editor(s): November 13, 2002
Received by editor(s) in revised form: May 19, 2004
Published electronically: February 14, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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