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On the zero-one-pole set of a meromorphic function. II. (English) Zbl 0707.30024
[For part I see the author in ibid. 12, No.1, 9-22 (1989; Zbl 0672.30028).]
Let f and g be meromorphic functions in the plane C. If f and g assume the value \(a\in C\cup \{\infty \}\) with the same multiplicities, we denote this by \(f=a\Leftrightarrow g=a\). The author proves a number of theorems. The following is typical:
Theorem. Let f and g be nonconstant meromorphic functions satisfying \(f=0\Leftrightarrow g=0\), \(f=1\Leftrightarrow g=1\) and \(f=\infty \Leftrightarrow g=\infty\). If \[ \limsup_{r\to \infty}\{\bar N(r,0,f)+\bar N(r,\infty,f)\}/T(r,f)<, \] then \(f\equiv g\) or fg\(\equiv 1\).
Reviewer: Fred Gross

MSC:
30D30 Meromorphic functions of one complex variable, general theory
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References:
[1] W. K. HAYMAN, Meromorphic functions, Oxford (1964). · Zbl 0115.06203
[2] M. OZAWA, On the zero-one set of an entire function, II, Kodai Math. J. Vol. No. 2 (1979), 194-199. · Zbl 0416.30026 · doi:10.2996/kmj/1138036016
[3] K. TOHGE, Meromorphic functions covering certain finite sets at the same points, Kodai Math. J. Vol. 11 No. 2 (1988), 249-279 · Zbl 0663.30024 · doi:10.2996/kmj/1138038877
[4] H. UEDA, Unicity theorems for meromorphic or entire functions, II, Kodai Math J. Vol. 6 No. 1 (1983), 26-36. · Zbl 0518.30029 · doi:10.2996/kmj/1138036659
[5] H. UEDA, On the zero-one-pole set of a meromorphic function, Kodai Math. J. Vol.12 No. 1 (1989), 9-22 · Zbl 0672.30028 · doi:10.2996/kmj/1138038985
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