# zbMATH — the first resource for mathematics

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
Full Text:
##### 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.