Cyclic polynomials and the multiplication matrices of their roots.

DOI10.1016/j.jpaa.2003.07.004zbMath1041.11069OpenAlexW1978555485MaRDI QIDQ1428109

Francisco Thaine

Publication date: 14 March 2004

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2003.07.004

zbMATH Keywords

characteristic polynomialcirculant matrixJacobi summultiplication matrixcyclotomic numberGaussian periodStickelberger elementcyclic polynomial

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Polynomials over finite fields (11T06) Cyclotomic extensions (11R18) Cyclotomy (11T22) Other abelian and metabelian extensions (11R20)

Related Items (3)

Explicit lifts of quintic Jacobi sums and period polynomials for \(\mathbb F_q\) ⋮ Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations ⋮ Davenport and Hasse's theorems and lifts of multiplication matrices of Gaussian periods

Cites Work

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• On Gaussian periods that are rational integers
• Jacobi sums and new families of irreducible polynomials of Gaussian periods
• Quintic Polynomials and Real Cyclotomic Fields with Large Class Number
• Connection Between Gaussian Periods and Cyclic Units
• Families of irreducible polynomials of Gaussian periods and matrices of cyclotomic numbers
• Cyclotomy, Higher Congruences, and Waring's Problem
• Properties that characterize Gaussian periods and cyclotomic numbers

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