Exceptional values in holomorphic families of entire functions

Details Exceptional values in holomorphic families of entire functions Exceptional values in holomorphic families of entire functions

2005-03-31

arxiv.org/abs/math/0503750v1

Michigan Math. J., 54, 3 (2006) 687-696

Mathematics

Complex Variables

12 pages

Scientific paper

We 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.

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