## 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 $$\frac{f'}{f}$$.

### MSC:

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

### Keywords:

transcendental entire function; meromorphic function; zeros
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