Related papers: Linear differential polynomials in zero-free merom…
The main result of the paper determines all real meromorphic functions of finite order in the plane for which the first derivative has finitely many zeros, while the function itself and one of its higher derivatives have finitely many…
A result is proved concerning meromorphic functions of finite order in the plane such that all but finitely many zeros of the second derivative are zeros of the first derivative.
We show that for a real transcendental meromorphic function f, the differential polynomial f'+f^m with m > 4 has infinitely many non-real zeros. Similar results are obtained for differential polynomials f'f^m-1. We specially investigate the…
It is shown that if $f$ or $1/f$ is a real entire function of infinite order of growth, with only real zeros, then $f''+\omega f$ has infinitely many non-real zeros for any $\omega > 0$.
Lower bounds are given for the number of non-real zeros of a second order linear differential polynomial with constant coefficients in a real entire function with finitely many non-real zeros.
Let f be a nonconstant meromorphic function in the plane and h be a nonconstant elliptic function. We show that if all zeros of f are multiple exept finitely many and T(r,h)=o{T(r,f)} as r tends to infinity, then f'=h has infinitely many…
The uniqueness problems on transcendental meromorphic or entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results have been obtained. In this paper, we study a…
In this article, we prove some normality criteria for a family of meromorphic functions having zeros with some multiplicity. Our main result involves sharing of a holomorphic function by certain differential polynomials. Our results…
A number of results are proved concerning non-real zeros of derivatives of real and strictly non-real meromorphic functions in the plane
Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = f(z+1) - f(z). A number of results are proved concerning the existence of zeros of g(z) or g(z)/f(z), in terms of the growth and the poles of f.
For differential equations $P(y^{(k)},y)=0,$ where $P$ is a polynomial, we prove that all meromorphic solutions having at least one pole are elliptic functions, possibly degenerate.
A number of results are proved concerning the existence of non-real zeros of derivatives of strictly non-real meromorphic functions in the plane.
In this paper we prove some normality criteria for a family of meromorphic functions, which involves the zeros of certain differential polynomials generated by the members of the family.
We consider the zeros distributions on the derivatives of difference polynomials of meromorphic functions, and present some results which can be seen as the discrete analogues of Hayman conjecture \cite{hayman1}, also partly answer the…
We consider transcendental meromorphic functions for which the zeros, 1-points and poles are distributed on three distinct rays. We show that such functions exist if and only if the rays are equally spaced. We also obtain a normal family…
In this paper, we investigate zeros of difference polynomials of the form $f(z)^nH(z, f)-s(z)$, where $f(z)$ is a meromorphic function, $H(z, f)$ is a difference polynomial of $f(z)$ and $s(z)$ is a small function. We first obtain some…
A number of results are proved concerning non-real zeros of derivatives of real meromorphic functions. In particular, the paper supersedes the previous arXiv submission "Non-real zeros of linear differential polynomials in real meromorphic…
We study the effect of finite difference operators of finite order on the distribution of zeros of polynomials and entire functions.
Every real Bank-Laine function of finite order, whose zeros are all real but neither bounded above nor bounded below, either has an explicit representation in terms of trigonometric functions or has zeros with exponent of convergence at…
In this note it is shown that two key results on transcendental singularities for meromorphic functions of finite lower order have refinements which hold under the weaker hypothesis that the logarithmic derivative has finite lower order.