Abstract
Letf 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 supr→∞n(r, a)/logM (r)≥1/2π for all except possibly one a∈C.
Funding Statement
Supported by a Heisenberg Fellowship of the Deutsche Forschungsgemeinschaft.
Citation
Walter Bergweiler. "A quantitative version of Picard's theorem." Ark. Mat. 34 (2) 225 - 229, October 1996. https://doi.org/10.1007/BF02559545
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