Related papers: Non-real zeros of derivatives of meromorphic funct…

A number of results are proved concerning the existence of non-real zeros of derivatives of strictly non-real meromorphic functions in the plane.

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…

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.

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 $\omega > 0$.

The main result establishes an estimate for the growth of a real meromorphic function $f$ on the unit disc $\Delta$ such that: (i) at least one of $f$ and $1/f$ has finitely many poles and non-real zeros in $\Delta$; (ii)~$f^{(k)}$ has…

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.

The main result of this paper shows a totally new necessary and sufficient condition to determine both real and complex zeros of derivative of all entire and meromorphic functions of one complex variable in the extended complex plane. By…

The paper proves a special case of a conjecture of Hellerstein, Shen and Williamson concerning non-real zeros of derivatives of real meromorphic functions.

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.

The paper determines all meromorphic functions with finitely many zeros in the plane having the property that a linear differential polynomial in the function, of order at least 3 and with rational functions as coefficients, also has…

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…

The real and complex zeros of some special entire functions such as Wright, hyper-Bessel, and a special case of generalized hypergeometric functions are studied by using some classical results of Laguerre, Obreschkhoff, P\'olya and Runckel.…

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…

In this paper, we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.

We characterize meromorphic function fields closed by partial derivatives in n variables.

The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…

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…

In this article, various results will be demonstrated that enable the delimitation of a zero-free region for holomorphic functions on a set $K$, studying the behavior of their imaginary or real part on the boundary of $K$. These findings…

Two theorems on the asymptotic distribution of zeros of sequences of analytic functions are proved. First one relates the asymptotic behavior of zeros to the asymptotic behavior of coefficients. Second theorem establishes a relation between…