We prove a result on the frequency of zeros of f ◦ g −Q, where g is a transcendental entire function of finite lower order, and f and Q are meromorphic functions in the plane such that f has finite order and the growth of the target function Q is controlled by that of g. The particular case f = Q is then investigated further.

We find all nonrational meromorphic solutions of the equation ww′′ − (w′)2 = α(z)w + β(z)w′ + γ (z), where α, β, and γ are rational functions of z. In so doing, we answer a question of Hayman by showing that all such solutions have finite order. Apart from special choices of the coefficient functions, the general solution is not meromorphic and contains movable branch points. For some choices f...

The behavior of meromorphic solutions of differential equations has been the subject of much study. Research has concentrated on the value distribution of meromorphic solutions and their rates of growth. The purpose of the present paper is to show that a thorough search will yield a list of all meromorphic solutions of a multi-parameter ordinary differential equation introduced by Hayman. This ...

Abstract In this paper, we deduce the form of a nonconstant meromorphic function f when some power shares certain set counting multiplicities in weak sense with k-th derivative power. The results paper generalize due to Lahiri and Zeng [Afr. Mat. 27 (2016), 941-947].

In this brief note, we will investigate the number of points of bounded height in a projective variety defined over a function field, where the function field comes from a projective variety of dimension greater than or equal to 2. A first step in this investigation is to understand the p-adic analytic properties of the height zeta function. In particular, we will show that for a large class of...