For a germ of a meromorphic function f = P Q , we offer notions of the mono-dromy operators at zero and at infinity. If the holomorphic functions P and Q are non-degenerated with respect to their Newton diagrams, we give an analogue of the formula of Varchenko for the zeta-functions of these monodromy operators. A polynomial f of (n + 1) complex variables of degree d determines a meromorphic fu...

In this paper, we investigate the relationship between small functions and differential polynomials gf (z) = d2f ′′ + d1f ′ + d0f , where d0 (z) , d1 (z) , d2 (z) are meromorphic functions that are not all equal to zero with finite order generated by solutions of the second order linear differential equation f ′′ + Af ′ +Bf = F, where A, B, F 6≡ 0 are finite order meromorphic functions having o...

is called Riemann’s Theorem and guarantees the existence of functions whose poles can only occur at certain places. In fact, if D = ∑ ni(Pi) − ∑ mj(Qj), then H(D) consists of all functions f with zeros of order ≥ mj at Qj and poles of order ≤ ni at Pi. Riemann’s original motivation was to construct meromorphic functions on compact Riemann surfaces. For example, the meromorphic functions on a to...

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 the present investigation we define a new class of meromorphic functions on the punctured unit disk Δ∗ := {z ∈ C : 0 < |z| < 1} by making use of the generalized Dziok–Srivastava operator Hl m [α1]. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neigh...

By using Tsuji's characteristic, we investigate uniqueness of meromorphic functions in an angular domain dealing with the shared set, which is different from the set of the paper (Lin et al., 2006) and obtain a series of results about the unique range set of meromorphic functions in angular domain.

The object of the present paper is to derive a property of certain meromorphic functions in the punctured unit disk. Our main theorem contains certain sufficient conditions for starlikeness and close-to-convexity of order α of meromorphic functions. 2000 Mathematics Subject Classification. 30C45.

 In this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{T}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. We use a strong convolution technique and derive inclusion results. A radius problem and some other interesting properties of these classes are discussed.