A quantitative version of Picard's theorem |
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| Authors: | Walter Bergweiler |
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| Institution: | 1. Fachbereich Mathematik, Technische Universit?t Berlin, Stra?e des 17. Juni 136, D-10623, Berlin, Germany
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| Abstract: | Letf be an entire function of order at least 1/2,M(r)=max|
z|=r|f(z)|, andn(r, a) the number of zeros off(z)-a in |z|≤r. It is shown that lim sup
r→∞
n(r, a)/logM (r)≥1/2π for all except possibly onea∈C.
Supported by a Heisenberg Fellowship of the Deutsche Forschungsgemeinschaft. |
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| Keywords: | |
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