Related papers: Entire periodic functions with plane zeros

The paper determines all meromorphic functions with finitely many zeros in the plane having the property that a linear differential polynomial in the function, of order at least 3 and with rational functions as coefficients, also has…

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…

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

In this paper, we consider the physical meaning of the zeros and poles of partition function. We consider three different systems, including the harmonic oscillator in one dimension, Riemann zeta function and the quasinormal modes of black…

We give necessary and sufficient conditions for a divisor in a tube domain to be the divisor of a holomorphic function with almost--periodic modulus.

In this paper, we seek to explore under what conditions the periodicity of an entire function $ f(z) $ follows from the periodicity of a differential polynomial in $ f(z) $. We improve and generalize some earlier results and we give other…

The concept of a sequence of exact zero-divisors on a noetherian local ring is defined and studied. Some properties of sequences of exact zero-divisors are compared with regular sequences.

A number of results are proved concerning non-real zeros of derivatives of real and strictly non-real meromorphic functions in the plane

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…

In this paper we initiate the study of the total zero-divisor graphs over commutative rings with unity. These graphs are constructed by both relations that arise from the zero-divisor graph and from the total graph of a ring. We…

We study zeros distribution for meromorphic functions of the form $\sum\limits_n \dfrac{c_n}{(z-t_n)^2}$, where $\sum\limits_n \dfrac{|c_n|}{|t_n|^2} <\infty$. We prove an analog of the classical Keldysh theorem and discuss a relation…

A number of results are proved concerning the existence of non-real zeros of derivatives of strictly non-real meromorphic functions in the plane.

In this work we establish some polynomials and entire functions have only real zeros. These polynomials generalize q-Laguerre polynomials $L_{n}^{(\alpha)}(x;q)$, while the entire functions are generalizations of Ramanujan's entire function…

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.

We derive a useful result about the zeros of the $k$-polar polynomials on the unit circle; in particular we obtain a ring shaped region containing all the zeros of these polynomials. Some examples are presented.

We consider a certain class of multiplicative functions $f: \mathbb N \rightarrow \mathbb C$ and study the distribution of zeros of Dirichlet polynomials $F_N(s)= \sum_{n\le N} f(n)n^{-s}$ corresponding to these functions. We prove that the…

We study meromorphic functions in a strip almost periodic with respect to the spherical metric. Then we get a complete description of zeros and poles for this class of functions, find a condition for a meromorphic almost periodic function…

We give a condition under which a divisor X in a bounded convex domain of finite type D in C^n is the zero set of a function in a Hardy space H^p(D) for some p \textgreater{} 0. This generalizes Varopoulos' result [Zero sets of H^p…

We prove that if $\sum_n n! c_n z^n$ is entire and $c_n$ does not terminate, then $\sum_n c_n z^n$ has infinitely many zeros. We then use this result to give alternative proofs that the Le Roy functions $f_r(z)=\sum_{n=0}^\infty…