Algebraic curves P(x)-Q(y)=0 and functional equations

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dc.creatorPakovich, F.
dc.date2008-04-04
dc.date2008-07-29
dc.date.accessioned2026-07-07T09:53:05Z
dc.date.available2026-07-07T09:53:05Z
dc.descriptionIn this paper we give several conditions implying the irreducibility of the algebraic curve P(x)-Q(y)=0, where P,Q are rational functions. We also apply the results obtained to the functional equations P(f)=Q(g) and P(f)=cP(g), where c\in C. For example, we show that for a generic pair of rational functions P,Q the first equation has no non-constant solutions f,g meromorphic on C whenever (°P-1)(°Q-1) \geq 2.
dc.descriptionfinal version accepted by Complex Var. and Elliptic Equ
dc.identifierhttps://arxiv.org/abs/0804.0736
dc.identifierhttp://arxiv.org/abs/0804.0736
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165829
dc.subjectComplex Variables
dc.subjectAlgebraic Geometry
dc.subject30D05; 39B32
dc.titleAlgebraic curves P(x)-Q(y)=0 and functional equations
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