In this contribution we announce a complete classification and new exotic phenomena of the meromorphic structure of ζ-functions associated to conic manifolds proved in [37]. In particular, we show that the meromorphic extensions of these ζfunctions have, in general, countably many logarithmic branch cuts on the nonpositive real axis and unusual locations of poles with arbitrarily large multipli...

The object of the present paper is to investigate a family of integral operators defined on the space of meromorphic functions. By making use of these novel integral operators, we introduce and investigate several new subclasses of starlike, convex, close-to-convex, and quasiconvex meromorphic functions. In particular, we establish some inclusion relationships associated with the aforementioned...

In the present investigation, the authors define a new class of meromorphic functions defined in the punctured unit disk ∆∗ := {z ∈ C : 0 < |z| < 1} by making use of the generalized Dziok-Srivastava operator L1 η,l,m. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic fu...

In this paper, we investigate the growth of meromorphic solutions to a complex higher order linear differential equation whose coefficients are meromorphic functions of [p, q]-orders. We get the results about the lower [p, q]-order of solutions of the equation. Moreover, we investigate the [p, q]-convergence exponent and the lower [p, q]-convergence exponent of distinct zeros of f(z)− φ(z). AMS...

where Aj(z) (j = 0, 1, . . . , k) are meromorphic functions with finite order. Under some conditions on the coefficients, we show that all meromorphic solutions f 6≡ 0 of the above equations have an infinite order and infinite lower order. Furthermore, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros. We improve the results due to Kwon; C...

Abstract. The purpose of the present paper is to introduce new classMB(α, λ, q, s, A,B) of meromorphic functions defined by using a meromorphic analogue of the Choi-Saigo-Srivastava operator for the generalized hypergeometric function and investigate a number of inclusion relationships and radius problem of this class.The subordination relations, distortion theorems, and inequality properties a...

In this paper, we investigate the growth of solutions of the linear differential equation 0 = Bf f A f      , where ) (z A and 0) )( (  z B are meromorphic functions. More specifically, we estimate the lower bounded of hyperorder of solutions of the equation with respect to the conditions of ) (z A and 0) )( (  z B if solutions 0 ( f ) of the equation is of infinite order. keywords: ...

We show that if f is a transcendental meromorphic function with a finite number of poles and f has a cycle of Baker domains of period p, then there exist C > 1 and r0 > 0 such { z : 1 C r < |z| < Cr } sing(f−p) ∅, for r r0. We also give examples to show that this result fails for transcendental meromorphic functions with infinitely many poles.

Abstract. In this paper, we investigate the higher-order linear differential equations with meromorphic coefficients. We improve and extend a result of M.S. Liu and C.L. Yuan, by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen, and the extended Winman-Valiron theory which proved by J. Wang and H.X. Yi. In addition, we also consider th...

In this paper, we show that if two non-constant meromorphic functions f and g satisfy E(aj , k, f) = E(aj , k, g) for j = 1, 2, . . . , 5, where aj are five distinct small functions with respect to f and g, and k is a positive integer or ∞ with k ≥ 14, then f ≡ g. As a special case this also answers the longstanding problem on uniqueness of meromorphic functions concerning small functions.