‎we mainly discuss the existence of meromorphic (entire) solutions of‎ ‎certain type of non-linear difference equation of the form‎: ‎$f(z)^m+p(z)f(z+c)^n=q(z)$‎, ‎which is a supplement of previous‎ ‎results in [k‎. ‎liu‎, ‎l. z‎. ‎yang and x‎. ‎l‎. ‎liu‎, ‎existence of entire solutions of nonlinear difference‎ ‎equations‎, ‎czechoslovak math. j. 61 (2011)‎, no. 2, ‎565--576‎, and x‎. ‎g‎. ‎qi‎...

We will establish a theorem on value distribution of L-functions in the Selberg class, which shows how an L-function and a meromorphic function are uniquely determined by their c-values and which, as a consequence, proves a result on the unicity of the Riemann zeta function. L-functions, with the Riemann zeta function as a prototype, are important objects in number theory, and value distributio...

This thesis consists of three contributions to the theory of complex approximation on Riemann surfaces. It is known that if E is a closed subset of an open Riemann surface R and f is a holomorphic function on a neighbourhood of E, then it is “usually” not possible to approximate f uniformly by functions holomorphic on all of R. In Chapter 2, we show, however, that for every open Riemann surface...

In this paper we establish some results concerning the partial sums of meromorphic p-valent starlike functions and meromorphic p-valent convex functions.

in this paper, we consider a new class of analytic functions in the unit disk using polynomials of order alpha. we give some sufficient conditions for functions belonging to this class.

In this article we study the growth of meromorphic solutions of high order linear differential equations with meromorphic coefficients of (p, q)order. We extend some previous results due to Beläıdi, Cao-Xu-Chen, Kinnunen, LiuTu -Shi, and others.

The main purpose of this paper is to introduce and investigate a certain subclass of meromorphic close-to-convex functions. Such results as coefficient inequalities, convolution property, inclusion relationship, distortion property, and radius of meromorphic convexity are derived.

We derive an explicit c-function expansion of a basic hypergeometric function associated to root systems. The basic hypergeometric function in question was constructed as explicit series expansion in symmetric Macdonald polynomials by Cherednik in case the associated twisted affine root system is reduced. Its construction was extended to the nonreduced case by the author. It is a meromorphic We...

In this paper, we give a short survey of results related to the reciprocity laws over the field C. We announce a visual topological proof of Parshin’s multidimensional reciprocity laws over C. We introduce the logarithmic functional, whose argument is an n-dimensional cycle in the group (C∗)n+1. It generalizes the usual logarithm, which can be considered as the zero-dimensional logarithmic func...

This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Hunter-Saxton (HS2) hierarchy through an initial value problem. Our main tools include polynomial recursive formalism, hyperelliptic curve with finite number genus, Baker-Akhiezer functions, meromorphic function, Dubrovin-type equations auxiliary ...