Related papers: Meromorphic Extendibility and Rigidity of Interpol…

We investigate when a meromorphic connection on a smooth rigid analytic variety $X$ gives rise to a coadmissible $\mathcal{D}_X$-cap-module, and show that this is always the case when the roots of the corresponding $b$-functions are all of…

Using the locally compact abelian group $\BT \times \BZ$, we assign a meromorphic function to each ideal triangulation of a 3-manifold with torus boundary components. The function is invariant under all 2--3 Pachner moves, and thus is a…

In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…

It is proved that CR functions on a quadratic cone M in $\C^n$, n>1, admit one-sided holomorphic extension if and only if M does not have two-sided support, a geometric condition on M which generalizes minimality in the sense of Tumanov. A…

Consider a continuous one parameter family of circles in complex plane that contains two circles lying in the exterior of one another. Under mild assumptions on the family, we prove that if a continuous function on the union of the above…

In this paper, a normality criterion concerning a sequence of meromorphic functions and their differential polynomials is obtained. Precisely, we have proved: Let $\left\{f_j\right\}$ be a sequence of meromorphic functions in the open unit…

The standard twist of $L$-functions plays a fundamental role in the Selberg class theory. It is defined as an absolutely convergent Dirichlet series and admits meromorphic continuation beyond the half-plane of absolute convergence.…

Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = f(z+1) - f(z). A number of results are proved concerning the existence of zeros of g(z) or g(z)/f(z), in terms of the growth and the poles of f.

Inspired by the work of Bank on the hypertranscendence of $\Gamma e^h$ where $\Gamma$ is the Euler gamma function and $h$ is an entire function, we investigate when a meromorphic function $fe^g$ cannot satisfy any algebraic differential…

In 2002 A.\ Hartmann and X.\ Massaneda obtained necessary and sufficient conditions for interpolation sequences for classes of analytic functions in the unit disc such that $\log M(r,f)=O((1-r)^{-\rho})$, $0<r<1$, $\rho \in (0 , +\infty)$,…

This article extends classical one variable results about Euler products defined by integral valued polynomial or analytic functions to several variables. We show there exists a meromorphic continuation up to a presumed natural boundary,…

Suppose f is a $C^{1+\alpha}$ surface diffeomorphism, and m is an equilibrium measure of a Holder continuous potential. We show that if m has positive metric entropy, then f is measure theoretically isomorphic to the product of a Bernoulli…

In this article we consider functions $f$ meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions. This condition simplifies and generalizes known conditions. We…

Given a dissipative operator $A$ on a complex Hilbert space $\mathcal{H}$ such that the quadratic form $f\mapsto \mbox{Im}\langle f,Af\rangle$ is closable, we give a necessary and sufficient condition for an extension of $A$ to still be…

A univalent meromorphic function defined on $\Delta:= \{z \in \mathbb{C}: 1<|z|<\infty \}$ with univalent inverse defined on $\Delta$ is bi-univalent meromorphic in $\Delta$. For certain subclasses of meromorphic bi-univalent functions,…

It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the hole complex plane. In this paper, certain cases of specific (non-real analytic) smooth functions…

We show that if a meromorphic function has a direct singularity over infinity, then the escaping set has an unbounded component and the intersection of the escaping set with the Julia set contains continua. This intersection has an…

In this paper, we obtain the meromorphic continuation of a q-analogue of multiple zeta function using an elementary formula called translation formula. We then obtain the matrix representation of the translation formula and using it, we…

There are three new things in this paper about the open symmetrized bidisk $\mathbb G = \{(z_1+z_2, z_1z_2) : |z_1|, |z_2| < 1\}$. They are motivated in the Introduction. In this Abstract, we mention them in the order in which they will be…

We consider the class $\Sigma(p)$ of univalent meromorphic functions $f$ on $\ID$ having simple pole at $z=p\in[0,1)$ with residue 1. Let $\Sigma_k(p)$ be the class of functions in $\Sigma(p)$ which have $k$-quasiconformal extension to the…