Related papers: Some Remarks on Shanks-type Conjectures

We investigate the existence of random close and random loose packing limits in two-dimensional packings of monodisperse hard disks. A statistical mechanics approach-- based on several approximations to predict the probability distribution…

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…

A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the…

Recently, the authors have proved the finiteness of common zeros of two iterated rational maps under some compositional independence assumptions. In this article, we advance towards a question of Hsia and Tucker on a Zariski non-density of…

We study Dirichlet-type spaces $\mathfrak{D}_{\alpha}$ of analytic functions in the unit bidisk and their cyclic elements. These are the functions $f$ for which there exists a sequence $(p_n)_{n=1}^{\infty}$ of polynomials in two variables…

We note that the recent polynomial proofs of the spherical and complex plank covering problems by Zhao and Ortega-Moreno give some general information on zeros of real and complex polynomials restricted to the unit sphere. As a corollary of…

By combining computer simulations and a unit cell model approach, we study the apparent bimodality of local structural ordering in a system of confined hard disks. It is shown that a two-dimensional (2D) array of hard disks confined…

In this note we extend the Gauss-Lucas theorem on the zeros of the derivative of a univariate polynomial to the case of sequences of univariate polynomials whose almost all zeros lie in a given convex bounded domain in C.

A short note on bounds on distance to variety of a point in terms of the Taylor coefficients at the point.

We demonstrate counterexamples to Wilmshurst's conjecture on the valence of harmonic polynomials in the plane, and we conjecture a bound that is linear in the analytic degree for each fixed anti-analytic degree. Then we initiate a…

We consider the problem of determining the maximum number of common zeros in a projective space over a finite field for a system of linearly independent multivariate homogeneous polynomials defined over that field. There is an elaborate…

This paper investigates asymptotic distribution of complex zeros of random polynomials $P_n(z):=\sum_{k=0}^{n}b(k)\xi_k z^k$, as $n\to\infty$, where $b$ is a regularly varying function at infinity with index $\alpha\in \mathbb{R}$ and…

We consider multilinear Littlewood polynomials, polynomials in $n$ variables in which a specified set of monomials $U$ have $\pm 1$ coefficients, and all other coefficients are $0$. We provide upper and lower bounds (which are close for $U$…

We characterize certain weighted Hardy spaces on the unit disk and completely describe their dual spaces.

We investigate asymptotic polynomial approximation for a class of weighted Bloch functions in the unit disc. Our main result is a structural theorem on asymptotic polynomial approximation in the unit disc, in the flavor of the classical…

Let $K$ be a quasidisk on the complex plane. We construct a sequence of monic polynomials $p_n=p_n(\cdot,K)$ with zeros on $K$ such that $||p_n||_K \le O(1) \mathrm{cap}(K)^n$ as $n\to\infty.$

We show that a nonvanishing analytic function on a domain in the unit disc can be approximated by (a scalar multiple of) a Blaschke product whose zeros lie on a prescribed circle enclosing the domain. We also give a new proof of the…

The derivative of a polynomial with all zeros on the unit circle has the zeros of its derivative on or inside the unit circle. It has been observed that in many cases the zeros of the derivative have a bimodal distribution: there are two…

We calculate the zeros of an exponential polynomial of some variables by a classical algorithm and quantum algorithms which are based on the method of van Dam and Shparlinski, they treated the case of two variables, and compare with the…

We study the problem of lifting of polynomial symplectomorphisms in characteristic zero to automorphisms of the Weyl algebra by means of approximation by tame automorphisms. We utilize -- and reprove -- D. Anick's fundamental result on…