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Estimates for the zeros of differences of meromorphic functions. (English) Zbl 1181.30016
Summary: Let $f$ be a transcendental meromorphic function, $g\left(z\right)=f\left(z+{c}_{1}\right)+f\left(z+{c}_{2}\right)-2f\left(z\right)$, and ${g}_{2}\left(z\right)=f\left(z+{c}_{1}\right)·f\left(z+{c}^{2}\right)-{f}^{2}\left(z\right)$. The exponents of convergence of zeros of $g\left(z\right)$, ${g}_{2}\left(z\right)$, $g\left(z\right)/f\left(z\right)$, and ${g}^{2}\left(z\right)/{f}^{2}\left(z\right)$ are estimated accurately.
MSC:
 30D35 Distribution of values (one complex variable); Nevanlinna theory
References:
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