Factorization of special harmonic polynomials of three variables Full article
| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2020, Volume: 17, Pages: 1299-1312 Pages count : 14 DOI: 10.33048/semi.2020.17.096 | ||
| Tags | Legendre functions, harmonic polynomials, factorization | ||
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| Affiliations |
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Funding (1)
| 1 | Омский филиал ФГБУН «Институт математики им. С.Л. Соболева СО РАН». | 0314-2019-0004 |
Abstract:
We consider homogeneous harmonic polynomials of real variables x,y,z that are eigenfunctions of the rotations about the axis z. They have the form (x±yi)^n p(x,y,z), where p is a rotation invariant polynomial. Let R_m be the family of the homogeneous rotation invariant polynomials p of degree m such that p is reducible over the rationals and (x+yi)^n p is harmonic for some n∈N. We describe R_m for m≤5 and prove that R_6 and R_7 are finite.
Cite:
Gichev V.M.
Factorization of special harmonic polynomials of three variables
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2020. V.17. P.1299-1312. DOI: 10.33048/semi.2020.17.096 WOS Scopus OpenAlex
Factorization of special harmonic polynomials of three variables
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2020. V.17. P.1299-1312. DOI: 10.33048/semi.2020.17.096 WOS Scopus OpenAlex
Dates:
| Submitted: | Nov 2, 2019 |
| Accepted: | Sep 8, 2020 |
| Published print: | Sep 8, 2020 |
| Published online: | Sep 8, 2020 |
Identifiers:
| Web of science: | WOS:000567363400001 |
| Scopus: | 2-s2.0-85099346106 |
| OpenAlex: | W3117561836 |