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
MR Author ID:
714371
Email:
hoshi@ruri.waseda.jp
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
