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On a question of Hong Xun Yi. (English) Zbl 1087.30028
The author studies the problem of uniqueness for meromorphic functions. Using a notation from the paper I. Lahiri [Nagoya Math. J. 161, 193–206 (2001; Zbl 0981.30023)], he obtains the following result:
Let \(S = \{z: z^n + a z^{n - 1} + b = 0\}\), where \(n\geq 7\) be a positive integer and \(a\), \(b\) be two nonzero constants such that \(z^n + a z^{n-1} + b = 0\) has no multiple root. If \(\Theta (\infty; f) + \Theta (\infty; g) > 1\) and \(E_f (S, 2) = E_g (S, 2)\), \(E_f(\{\infty \}, \infty ) = E_g (\{\infty \}, \infty )\) then \(f\equiv g\).
This uniqueness theorem modifies and in some sense improves a result of M.-L. Fang and I. Lahiri [Indian J. Math. 45, No. 2, 141–150 (2003; Zbl 1048.30014)] and answers a question of H.-X. Yi [Bull. Aust. Math. Soc. 52, No. 2, 215–224 (1995; Zbl 0844.30022)].
Reviewer: Josef Kalas (Brno)

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