Abstract
We say two meromorphic functions f(z) and g(z) share the finite complex value c if f(z) — c and g(z) — c have the same zeros. We will state whether a value is shared CM (counting multiplicities), IM (ignoring multiplicities), or by DM (by different multiplicities at one point or more). In this paper all functions will be assumed to be meromoφhic in the whole complex plane, unless stated otherwise. R. Nevanlinna [7, p. 109] proved that if/and g share five values IM, then either f—govf and g are both constants. He also found [7, Chapter V] the particular form of all pairs /, g that share four values CM and all pairs/, g that share three values CM. L. A. Rubel and C. C. Yang proved the following result:
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