Exceptional values in holomorphic families of entire functions

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dc.creatorEremenko, Alexandre
dc.date2005-03-31
dc.date.accessioned2026-07-07T09:55:28Z
dc.date.available2026-07-07T09:55:28Z
dc.descriptionWe study Picard's exceptional values of holomorphic one-parametric families of entire functions. Our first result shows that the set of parameter values for which zero is a Picard value can be an arbitrary closed set of zero logarithmic capacity. This answers a question of Julia. Second, we show that if a function has a Picard exceptional value for all values of parameter in some region of the plane then this Picard value is a holomorphic function in the complement of some discrete set E, tending to infinity as the papameter tends to E.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0503750
dc.identifierhttp://arxiv.org/abs/math/0503750
dc.identifierMichigan Math. J., 54, 3 (2006) 687-696
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166642
dc.subjectComplex Variables
dc.subject20D20; 32A60; 32U30
dc.titleExceptional values in holomorphic families of entire functions
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