Further results on fixpoints and zeros of entire functions

Abstract

In this paper, a quantitative estimation on the number of zeros of the function f ∘ g ( z ) − α ( z ) f \circ g(z) - \alpha (z) is derived, where f f and g g are transcendental entire functions and α ( z ) \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 n of f n {f_n} ( n n th iterate of f f ) is obtained.