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Unicity theorems for meromorphic or entire functions. II. (English) Zbl 0844.30022

For part I see the author in Acta Math. Sin., New Ser. 10, No. 2, 121-131 (1994; Zbl 0806.30022).
Let \(f(z)\) and \(g(z)\) be meromorphic functions, and \(E_f(S)\) and \(E_g(S)\) denote the inverse images of the set \(S\) under \(f\) and \(g\) respectively. The author proves that there exists a finite set \(S\) with 11 elements such that for any two non-constant meromorphic functions \(f\) and \(g\), the conditions \(E_f(S)= E_g(S)\) and \(E_f(\{\infty\})= E_g(\{\infty\})\) imply \(f\equiv g\). As a special case, if \(f\) and \(g\) are entire functions, then the result answers a question posed by F. Gross [Lect. Notes Math. 599, 51-67 (1977; Zbl 0357.30007)].
Reviewer: He Yuzan (Beijing)

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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References:

[1] Yi, Bull. Austral. Math. Soc. 49 pp 257– (1994)
[2] Yi, Chinese Ann. Math. Ser. A 9A pp 434– (1988)
[3] DOI: 10.1007/BF01110921 · Zbl 0217.38402
[4] Gross, Complex Analysis (1977)
[5] Hayman, Meromorphic functions (1964)
[6] DOI: 10.2183/pjab.58.17
[7] Nevanlinna, Le théoréme de Picard-Borel et la théorie des fonctions méromorphes (1929)
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