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Keywords:
uniqueness; entire function; difference operator
uniqueness; entire function; difference operator
Summary:
We investigate the uniqueness of an entire function $f(z)$ sharing one finite value CM with its shift and its difference operator, in each case we find that $f(z)=h(z)\beta ^{\alpha z/c}$, where $ \alpha \not =0,$ $\beta >1$ and $h(z)$ is a periodic entire function of period $c$. Here, we say that two entire functions $f(z)$ and $g(z)$ share a value $a$ CM if $f(z)-a$ and $g(z)-a$ have the same zeros with same multiplicities.
References:
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