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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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.
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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