Zeros of differences of meromorphic functions. (English) Zbl 1114.30028

Let \(f\) be a function transcendental and meromorphic in the plane, and define \(g(z)\) by \(g(z)=\Delta f(z)=f(z+1)-f(z)\). A number of results are proved concerning the existence of zeros of \(g(z)\) or \(\frac{g(z)}{f(z)}\), in terms of the growth and the poles of \(f\). The results may be viewed as discrete analogues of existing theorems on the zeros of \(f'\) and \(\frac{f'}{f}\).


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