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Factorization of special harmonic polynomials of three variables

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Publication:6327954

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DOI10.33048/SEMI.2020.17.096arXiv1910.12265MaRDI QIDQ6327954

Author name not available (Why is that?)

Publication date: 27 October 2019

Abstract: We consider harmonic polynomials of real variables

x, y, z

that are eigenfunctions of the rotations about the axis

z

. They have the form

(x p m y i)^{n} p (x, y, z)

, where

p

is a rotation invariant polynomial. Let

{m a t h f r a k R}_{m}

be the family of the polynomials

p

of degree

m

which are reducible over the rationals. We describe

{m a t h f r a k R}_{m}

for

m l e q 5

and prove that

{m a t h f r a k R}_{6}

and

{m a t h f r a k R}_{7}

are finite.

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