# cyclotomic polynomial

## cyclotomic polynomial

[sī·klə‚täm·ik‚päl·ə′nōmē·əl]
(mathematics)
The n th cyclotomic polynomic is the monic polynomial of degree φ(n) [where φ represents Euler's phi function] whose zeros are the primitive n th roots of unity.
References in periodicals archive ?
n] is admissible if and only if the cyclotomic polynomial [[PHI].
The computation of the cyclotomic polynomial [[PHI].
This is done using the classical cyclotomic polynomials [[PHI].
This paper studies the cyclotomic polynomial [[PHI].
Section 2 describes our first interpretation for the cyclotomic polynomial, which applies much more generally to any monic polynomial in Z[x].
The special case where f(x) is the cyclotomic polynomial [[PHI].
The dependence (2) among the columns of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] has the same coefficients (up to scaling) as the cyclotomic polynomial, and the dependence (3) among the columns of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] has the same coefficients (up to scaling) as a nonzero cycle z = [[summation].
Thus it suffices to interpret the coefficients of cyclotomic polynomials for squarefree n.
They also thank Sam Elder, Nathan Kaplan, and Pieter Moree for helpful references on cyclotomic polynomials.
Bachman, On the Coefficients of Cyclotomic Polynomials Memoirs of the American Mathematical Society 106, 1993.
Elder, Flat Cyclotomic Polynomials, Colorado Math Circle Talk, January 2, 2010, http://www.
Kaplan, Flat cyclotomic polynomials of order three.
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