Related papers: Entire functions with two radially distributed val…
We consider transcendental entire functions of finite order for which the zeros and $1$-points are in disjoint sectors. Under suitable hypotheses on the sizes of these sectors we show that such functions must have a specific form, or that…
We consider the family of all functions holomorphic in the unit disk for which the zeros lie on one ray while the 1-points lie on two different rays. We prove that for certain configurations of the rays this family is normal outside the…
We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.
We propose the construction of entire functions with a given random collection of zeros. There are considered two particular cases. In the first one we are dealing with simple zeros. And the second corresponds to random zeros with random…
We investigate the zeros of two one-parameter families of harmonic functions and describe how the number of zeros depends on the parameter. Our functions have the property that all zeros lie on certain rays in the complex plane and thus we…
We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the Cauchy data are holomorphic on the complex…
In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].
We present methods that provide all zeroes and extrema of a function that do not require differentiation. Using point process theory, we are able to describe the locations of zeroes or maxima, their number, as well as their distribution…
We consider a class of weighted harmonic functions in the open upper half-plane known as $\alpha$-harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the…
We consider transcendental meromorphic functions for which the zeros, 1-points and poles are distributed on three distinct rays. We show that such functions exist if and only if the rays are equally spaced. We also obtain a normal family…
We announce conditions under which a given sequence of points on the complex plane is a subsequence of zeros of an entire function with weight restrictions on growth.
We construct and apply the classic balayage (sweeping out) of measures and subharmonic functions on closed system of rays in the complex plane with vertex at the origin, including measures and subharmonic functions and infinite order. The…
The real and complex zeros of some special entire functions such as Wright, hyper-Bessel, and a special case of generalized hypergeometric functions are studied by using some classical results of Laguerre, Obreschkhoff, P\'olya and Runckel.…
In these notes, we describe the recent progress in understanding the zero sets of two remarkable Gaussian random functions: the Gaussian entire function with invariant distribution of zeroes with respect to isometries of the complex plane,…
The uniqueness problems on transcendental meromorphic or entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results have been obtained. In this paper, we study a…
A general type of ray class fields of global function fields is investigated. The systematic computation of their genera leads to new examples of curves over finite fields with comparatively many rational points.
We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional…
In this paper we determine a class of entire functions using conditions on their odd and even parts. Further it is shown that the zeros of members of this class are localized in a very special way. This result allows us to treat a…
We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces…
In this article, various results will be demonstrated that enable the delimitation of a zero-free region for holomorphic functions on a set $K$, studying the behavior of their imaginary or real part on the boundary of $K$. These findings…