On spectral polynomials of the Heun equation. II

dc.creatorShapiro, Boris
dc.creatorTakemura, Kouichi
dc.creatorTater, Milos
dc.date2009-04-03
dc.date.accessioned2026-07-07T13:00:37Z
dc.date.available2026-07-07T13:00:37Z
dc.descriptionThe 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.description23 pages, 9 figures
dc.identifierhttps://arxiv.org/abs/0904.0650
dc.identifierhttp://arxiv.org/abs/0904.0650
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225891
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.subject34L20 (Primary), 30C15, 33E05 (Secondary)
dc.titleOn spectral polynomials of the Heun equation. II
dc.typetext

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