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It is well known that if two nonconstant meromorphic functions f and g on the complex plane ℂ have the same inverse images counted with multiplicities for four distinct values, then g is a Möbius transformation of f. In this paper, we will show that the above result remains valid if f and g share four distinct small functions counted with multiplicities truncated by 2. This is the best possible truncation level.
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Jul 1, 2009
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