In this article, a meromorphic function means meromorphic in the open complex plane. We assume that the reader is familiar with the Nevanlinna theory of meromorphic functions and the standard notations such as T r, f , m r, f , N r, f ,N r, f , and so on. Let f and g be two nonconstant meromorphic functions; a meromorphic function a z /≡∞ is called a small functions with respect to f provided t...

Our main result implies the following theorem: Let f be a transcendental meromorphic function in the complex plane. If f has finite order ρ, then every asymptotic value of f , except at most 2ρ of them, is a limit point of critical values of f . We give several applications of this theorem. For example we prove that if f is a transcendental meromorphic function then f ′fn with n ≥ 1 takes every...

Suppose Y is a regular covering of a graph X with covering transformation group π = Z. This paper gives an explicit formula for the L2 zeta function of Y and computes examples. When π = Z, the L2 zeta function is an algebraic function. As a consequence it extends to a meromorphic function on a Riemann surface. The meromorphic extension provides a setting to generalize known properties of zeta f...

Meromorphic functions with a given growth of spherical derivative on the complex plane are described in terms relative location a-points functions. The result obtained allows one to construct an example meromorphic function ? slow Nevanlinna characteristics and arbitrary derivative. In addition, based universality property Riemann zeta-function, we estimate ?(z).

The aim of the present paper is to study distributions of singular points of a zeta function which is expressed by an Euler product and is analytically continued as a meromorphic function of finite order. In this manuscript, we give a relation between the growth of the multiplicities for the norms of primitive elements and the order of the zeta function as a meromorphic function.

The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is presented, and then applied to prove a number of results on meromorphic solutions of complex difference equations. These results include a difference analogue...

Alexander [1] was the first to introduce certain subclasses of univalent functions examining the geometric properties of the image f(D) of D under f . The convex functions are those that map D onto a convex set. A function w = f(z) is said to be starlike if, together with any of its points w, the image f(D) contains the entire segment {tw : 0 ≤ t ≤ 1}. Thus we introduce the denotations S = {f ∈...

Motivated by the recent work on symmetric domains, this article investigates certain features of domain which are caused secant hyperbolic functions. Geometric characteristics analytic functions associated with discussed, include inclusion results, structural formula, sharp radii results such as radius starlikeness and convexity order α. It also finds a for ratios Euler numbers.