相关论文: Nevanlinna theory for the difference operator

In this short manuscript, we will put some light on the different outcomes when two non-constant meromorphic functions share a value with prescribed weight two.

The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…

A function $f$ from an Abelian group $(A,+)$ to an Abelian group $(B,+)$ is $(n, m, S)$ zero-difference (ZD), if $S=\{\lambda_\alpha \mid \alpha \in A\setminus\{0\}\}$ where $n=|A|$, $m=|f(A)|$ and $\lambda_\alpha=|\{x \in A \mid…

Let B be the open unit ball in C^2 and let a, b, c be three points in C^2 which do not lie in a complex line, such that the complex line through a and b meets B and such that <a|b> is different from 1 if one of the points a, b is in B and…

In this paper, we give a simple proof and strengthening of a uniqueness theorem of meromorphic functions which partially share 0, $\infty$ CM and 1 IM with their difference operators. Meanwhile, we partial solve a conjecture given by…

In this paper, we introduce the notion of an Evertse-Ferretti Nevanlinna constant and compare it with the birational Nevanlinna constant introduced by the authors in a recent joint paper. We then use it to recover several previously known…

This is a colloquium talk in CAU, Kiel delivered on June 7, 2024 on the occasion of Walter Bergweiler's retirement. Walter's work on meromorphic functions consists of two parts: generalizations of Picard's theorem to differential…

Let ${\mathcal S}$ be the class of analytic functions $f$ in the unit disk ${\mathbb D}$ with $f({\mathbb D}) \subset \overline{\mathbb D}$. Fix pairwise distinct points $z_1,\ldots,z_{n+1}\in \mathbb{D}$ and corresponding interpolation…

This paper aims to provide a Melnikov-like function that governs the existence of periodic solutions bifurcating from period annuli in certain families of second-order discontinuous differential equations of the form $\ddot{x}+\alpha\;…

It is proved that the Riemann zeta function does not satisfy any nontrivial algebraic difference equation whose coefficients are meromorphic functions $\phi$ with Nevanlinna characteristic satisfying $T(r, \phi)=o(r)$ as $r\to \infty$

Every rational Nevanlinna function in n variables is a Cayley inner function in n + 1 variables with one variable fixed in the upper half-plane.

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,…

This article treats Nevanlinna-Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of…

In this paper, by introducing the notion of "\textit{distributive constant}" of a family of hypersurfaces with respect to a projective variety, we prove a second main theorem in Nevanlinna theory for meromorphic mappings with arbitrary…

Let $f$ be a transcendental meromorphic function defined in the complex plane $\mathbb{C}$, and $\varphi(\not\equiv 0,\infty)$ be a small function of $f$. In this paper, We give a quantitative estimation of the characteristic function $T(r,…

Meromorphic solutions of non-linear differential equations of the form $f^n+P(z,f)=h$ are investigated, where $n\geq 2$ is an integer, $h$ is a meromorphic function, and $P(z,f)$ is differential polynomial in $f$ and its derivatives with…

The main result establishes an estimate for the growth of a real meromorphic function $f$ on the unit disc $\Delta$ such that: (i) at least one of $f$ and $1/f$ has finitely many poles and non-real zeros in $\Delta$; (ii)~$f^{(k)}$ has…

We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…

In this article we study the basic theoretical properties of Mellin-type fractional integrals, known as generalizations of the Hadamard-type fractional integrals. We give a new approach and version, specifying their semigroup property,…

The paper gives a precise asymptotic relation between higher order logarithmic difference and logarithmic derivatives for meromorphic functions with order strictly less then one. This allows us to formulate a useful Wiman-Valiron type…