Related papers: Random zeros entire functions

A method of constructing an entire function with given zeros and estimates of growth is suggested. It gives a possibility to describe zero sets of certain classes of entire functions of one and several variables in terms of growth of volume…

We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are…

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 $[2]$.

In this paper, we extend our earlier result (see [Y-2008]) on the distribution of normalized zero-sets of random entire functions to random entire functions with small random perturbation.

We give an explicit formula for the correlation functions of real zeros of a random polynomial with arbitrary independent continuously distributed coefficients.

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 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…

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,…

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 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…

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 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].

In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…

In this article we propose a new class of the even entire function connected with the product and series with the real coefficients. We address a sufficient condition for all real zeros for it. As a typical example, we give an answer to the…

This paper is concerned with the distribution of normalized zero-sets of random entire functions. The normalization of the zero-set is performed in the same way as that of the counting function for an entire function in Nevanlinna theory.…

In this short article we present some properties regarding the order and the type of an entire function.

Abstract. In this work we derive a sufficient condition to ensure certain genus 0 entire function that can have only negative zeros. We also apply this result to the Riemann hypothesis and generalized Riemann hypothesis for some primitive…

We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…

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…

On the plane, every random compact set with almost surely uncountable first projection intersects with a high probability the graph of some continuous function. Implication: every black noise over the plane fails to factorize when the plane…