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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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