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arXiv · 1910.12265

Factorization of special harmonic polynomials of three variables

Victor Gichev
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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 $(x\pm yi)^{n}p(x,y,z)$, where $p$ is a rotation invariant polynomial. Let ${\mathfrak R}_{m}$ be the family of the polynomials $p$ of degree $m$ which are reducible over the rationals. We describe ${\mathfrak R}_{m}$ for $m\leq5$ and prove that ${\mathfrak R}_{6}$ and ${\mathfrak R}_{7}$ are finite.

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Victor Gichev. 2019-10-27. Factorization of special harmonic polynomials of three variables. https://arxiv.org/abs/1910.12265

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