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A quantitative version of Picard's theorem

Walter Bergweiler Fachbereich Mathematik, Technische Universität Berlin

TBD mathscidoc:1701.332856

Arkiv for Matematik, 34, (2), 225-229, 1995.10
Let$f$be an entire function of order at least 1/2,$M(r)$=max_{|}$z$|=$r$|$f(z)$|, and$n(r, a)$the number of zeros of$f(z)-a$in |$z$|≤$r$. It is shown that lim sup_{$r$→∞}$n(r, a)$/log$M (r)$≥1/2π for all except possibly one$a$∈C.
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@inproceedings{walter1995a,
  title={A quantitative version of Picard's theorem},
  author={Walter Bergweiler},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203548574317665},
  booktitle={Arkiv for Matematik},
  volume={34},
  number={2},
  pages={225-229},
  year={1995},
}
Walter Bergweiler. A quantitative version of Picard's theorem. 1995. Vol. 34. In Arkiv for Matematik. pp.225-229. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203548574317665.
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