Related papers: On certain type of difference polynomials of merom…
This paper investigates the location of the zeros of a sequence of polynomials generated by a rational function with a denominator of the form $G(z,t)=P(t)+zt^{r}$, where the zeros of $P$ are positive and real. We show that every member of…
A crucial ingredient in the recent discovery by Ablowitz, Halburd, Herbst and Korhonen \cite{AHH}, \cite {HK-2} that a connection exists between discrete Painlev\'e equations and (finite order) Nevanlinna theory is an estimate of the…
n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for…
In this paper, we have investigated the sufficient conditions for periodicity of meromorphic functions and obtained two results directly improving the result of \emph{Bhoosnurmath-Kabbur} \cite{Bho & Kab-2013}, \emph{Qi-Dou-Yang} \cite{Qi &…
We study Hayman conjecture for different paired complex polynomials under certain conditions. In 2021, the zeros distribution of $f^{n}(z)L(g)-a(z)$ and $g^{n}(z)L(f)-a(z)$ was studied by Gao and Liu for $n\geq 3$. In this paper, we work on…
Let $D$ be a proper domain in the extended complex plane ${\mathbb C}_{\infty}:={\mathbb C}\cup \{\infty\}$, $M=M_+-M_-\not\equiv \pm \infty$ be a difference of non-trivial subharmonic functions $M_{\pm}\not\equiv \mp \infty$ on $D$,…
In this article we study F-pure thresholds (and, more generally, F-thresholds) of homogeneous polynomials in two variables over a field of characteristic p>0. Passing to a field extension, we factor such a polynomial into a product of…
If $f(x,y)$ is a real function satisfying $y>0$ and $\sum_{r=0}^{n-1}f(x+ry,ny)=f(x,y)$ for $n=1,2,3,\ldots$, we say that $f(x,y)$ is an invariant function. Many special functions including Bernoulli polynomials, Gamma function and Hurwitz…
For each positive integer n, we determine the set of symmetric functions f for which the congruence f(p/1,p/2,...,p/(p-1)) \equiv 0 mod p^n holds for all sufficiently large primes p. Our determination is conditional on a conjecture…
In this paper we study properties of hyperholomorphic functions on commutative finite algebras. It is investigated the Cauchy-Riemann type conditions for hyperholomorphic functions. We prove that a hyperholomorphic function on a commutative…
The meromorphic solutions $f$ with $\rho_2(f)<1$ of the non-linear difference equation \begin{align*} f^n(z)+P_d(z,f)=p_1e^{{\lambda_1}z}+p_2e^{{\lambda_2}z}+p_3e^{{\lambda_3}z}, \end{align*} are characterized in terms of exponential…
We consider a mock modular form $M_{\Delta}(\tau)$ that arises naturally from Ramanujan's Delta-function. It is a weight $-10$ harmonic Maass form whose nonholomorphic part is the "period integral function'' of $\Delta(\tau)$. The Hecke…
The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…
In this paper, we give results that partially prove a conjecture which was discussed in our previous work (arXiv:1307.4991). More precisely, we prove that as $n\to \infty,$ the zeros of the polynomial$${}_{2}\text{F}_{1}\left[…
We give explicit formulas for the number of meromorphic differentials on $\mathbb{CP}^1$ with two zeros and any number of residueless poles and for the number of meromorphic differentials on $\mathbb{CP}^1$ with one zero, two poles with…
Consider the following truncated Freud linear functional $\mathbf{u}_z$ depending on a parameter $z$, $$\langle\mathbf{u}_z,p\rangle=\int_0^\infty p(x)e^{-zx^4}dx,\quad z>0.$$ The aim of this work is to analyze the properties of the…
The objective of the paper is twofold. The first objective is to study the uniqueness problem of meromorphic function $f(z)$ when $f^{(1)}(z)$ shares two distinct finite values $a_1$, $a_2$ and $\infty$ CM with $\Delta_cf(z)$. In this…
We study functions f(z) holomorphic in the upper half plane and having no zeros when the imaginary part of z is between 0 and 1, and we obtain a lower bound for the modulus of f(z) in this strip. In our analysis we deal with scalar…
In this paper, monic polynomials orthogonal with deformation of the Freud-type weight function are considered. These polynomials fullfill linear differential equation with some polynomial coefficients in their holonomic form. The aim of…
Let $\Re_n$ be the set of all rational functions of the type $r(z) = p(z)/w(z),$ where $p(z)$ is a polynomial of degree at most $n$ and $w(z) = \prod_{j=1}^{n}(z-a_j)$, $|a_j|>1$ for $1\leq j\leq n$. In this paper, we set up some results…