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Factorization of special harmonic polynomials of three variables
- Publication Year :
- 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 $(x\pm yi)^{n}p(x,y,z)$, 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.
- Subjects :
- Rational number
33C60
Invariant polynomial
Degree (graph theory)
General Mathematics
Harmonic (mathematics)
Eigenfunction
Combinatorics
Factorization
Mathematics - Classical Analysis and ODEs
Classical Analysis and ODEs (math.CA)
FOS: Mathematics
Mathematics::Representation Theory
Rotation (mathematics)
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....107ff62760ed109a29a3209855f7b215