On spectral polynomials of the Heun equation. II
| dc.creator | Shapiro, Boris | |
| dc.creator | Takemura, Kouichi | |
| dc.creator | Tater, Milos | |
| dc.date | 2009-04-03 | |
| dc.date.accessioned | 2026-07-07T13:00:37Z | |
| dc.date.available | 2026-07-07T13:00:37Z | |
| dc.description | The well-known Heun equation has the form: Q(z)S''(z)+P(z)S'(z)+V(z)S(z)=0 where Q(z) is a cubic complex polynomial, P(z) and V(z) are polynomials of degrees at most 2 and 1 resp. One of the classical problems about the Heun equation is for a given positive integer N to find all possible linear polynomials V(z) such that the latter equation has a polynomial solution S(z) of degree N. Below we prove a conjecture of the 2nd author claiming that the union of roots of such V(z)'s for a given N tends when N->oo to a certain compact connecting the three roots of Q(z) and given by the condition that a certain natural abelian integral is real-valued. | |
| dc.description | 23 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/0904.0650 | |
| dc.identifier | http://arxiv.org/abs/0904.0650 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225891 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34L20 (Primary), 30C15, 33E05 (Secondary) | |
| dc.title | On spectral polynomials of the Heun equation. II | |
| dc.type | text |