Related papers: Some results in the uniqueness of meromorphic func…
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.
It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. But, in the case of general ($C^{\infty}$) smooth functions, the meromorphic…
The existence of meromorphic solutions to various difference equations has been extensively studied in recent years, the precise functional forms of such solutions -- particularly when the function and its difference operators share values…
The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated. The $\varphi$-order is used as a general growth indicator, which covers the growth spectrum between the…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
We give an alternative and simpler method for getting pointwise estimate of meromorphic solutions of homogeneous linear differential equations with coefficients meromorphic in a finite disk or in the open plane originally obtained by Hayman…
In this article, we study the growth of meromorphic solutions of linear delay-differential equation of the form \begin{equation*} \sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}(z)f^{(j)}(z+c_{i})=F(z), \end{equation*}% where $A_{ij}(z)$ $(i=0,1,\ldots…
In this paper, we describe the automorphic properties of the Fourier coefficients of meromorphic Jacobi forms. Extending results of Dabholkar, Murthy, and Zagier, and Bringmann and Folsom, we prove that the canonical Fourier coefficients of…
In this contribution we announce a complete classification and new exotic phenomena of the meromorphic structure of $\z$-functions associated to conic manifolds proved in \cite{KLP1}. In particular, we show that the meromorphic extensions…
This paper attempts to describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions. The reader is not expected to be familiar with the iteration theory of…
The Mittag-Leffler function plays an important role in Geometric Function Theory, particularly in the study of analytic and meromorphic function classes. Among its various generalizations, the Barnes-Mittag-Leffler function stands out due…
In this paper, we mainly propose improvements of the logarithmic difference lemma for meromorphic functions in several complex variables, and then investigate meromorphic solutions of partial difference equations from the viewpoint of…
We prove a Closing Lemma for nonuniformly hyperbolic measures of meromorphic maps. We prove also a theorem of approximation of the dynamics of such measures by Bernoulli coding maps.
This note reviews some of the recent work on biharmonic conformal maps (see \cite{OC}, Chapter 11, for a detailed survey). It will be focused on biharmonic conformal immersions and biharmonic conformal maps between manifolds of the same…
In this survey, we present recent results of the authors about non-meromorphic modular objects known as polar harmonic Maass forms. These include the computation of Fourier coefficients of meromorphic modular forms and relations between…
The purpose of this paper has twofold. The first is to prove a unicity theorem for meromorphic mappings of a complete K\"{a}hler manifold M in P^n(C) sharing few hypersurfaces. The second is to give a unicity theorem for the case of…
We discuss meromorphic functions on the complex plane which are Brody curves regarded as holomorphic maps to P_1, i.e., which have bounded spherical derivative.
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 meromorphic function on a compact complex analytic manifold defines a $\bc\infty$ locally trivial fibration over the complement of a finite set in the projective line $\bc\bp^1$. We describe zeta-functions of local monodromies of this…
This is a survey of results on the following problem. Consider a simply connected Riemann surface spread over the Riemann sphere. How are the properties of the uniformizing function of this surface related to the geometric properties of the…