Abstract
In this paper, a quantitative estimation on the number of zeros of the function $f \circ g(z) - \alpha (z)$ is derived, where $f$ and $g$ are transcendental entire functions and $\alpha (z)$ a nonconstant polynomial. As an application of this and a further step towards an affirmative answer to a conjecture of Baker, a quantitative estimation on the number of period points of exact order $n$ of ${f_n}$ ($n$th iterate of $f$) is obtained.
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