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...

We describe an algorithm deciding if the annihilating ideal of the meromorphic function 1 f , where f = 0 defines an arrangement of hyperplanes, is generated by linear differential operators of order 1. The algorithm is based on the comparison of two characteristic cycles and uses a combinatorial description due to Àlvarez-Montaner, Garćıa–López and Zarzuela of the characteristic cycle of the D...

* Correspondence: [email protected]. com School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China Full list of author information is available at the end of the article Abstract In this article, we investigate the uniqueness problems of difference operators of two meromorphic functions. Uniqueness of a meromorphic function f and its difference operator with the ...

The aim of the present paper is to study the relations between the prime distribution and the zero distribution for generalized zeta functions which are expressed by an Euler products and are analytically continued as meromorphic functions of finite order. In this paper, we give an inequality between the order of the zeta function as a meromorphic function and the growth of the multiplicity in ...

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.

0. abstract Regarding the resolution of singularities for the differential equations of Painlevé type, there are important differences between the second-order Painlevé equations and those of higher order. Unlike the second-order case, in higher order cases there may exist some meromorphic solution spaces with codimension 2. In this paper, we will give an explicit global resolution of singulari...

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...

Solutions to the Riemann-Hilbert problems with irregular singularities naturally associated to semisimple Frobenius manifold structures on Hurwitz spaces (moduli spaces of meromorphic functions on Riemann surfaces) are constructed. The solutions are given in terms of meromorphic bidifferentials defined on the underlying Riemann surface. The relationship between different classes of Frobenius ma...

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...