Related papers: On zeros of Boubaker polynomials

We prove an equidistribution result for the zeros of polynomials with integer coefficients and simple zeros. Specifically, we show that the normalized zero measures associated with a sequence of such polynomials, having small height…

We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval $(-1,1)$ are asymptotically independent of the zeros outside of this interval, and that the…

We consider multivariable polynomials over a fixed number field, linear in some of the variables. For a system of such polynomials satisfying certain technical conditions we prove the existence of search bounds for simultaneous zeros with…

This paper addresses the problem of deciding the lower-boundedness of an arbitrary real polynomial p in n variables.

We give a survey of the analytic theory of matrix orthogonal polynomials.

We discuss invariants in equivariant birational geometry.

In this paper, we prove a theorem on the distribution of primes in cubic progressions on average.

We present a method for the solution of polynomial equations. We do not intend to present one more method among several others, because today there are many excellent methods. Our main aim is educational. Here we attempt to present a method…

We discuss the zero sets of two-variable polynomials as they relate to an approximation problem in the Hardy space on the bidisk.

This note gives an elementary exposition of a variant of the spread polynomials in terms of Fibonacci and Lucas polynomials.

Sobolev orthogonal polynomials have been studied extensively in the past 20 years. The research in this field has sprawled into several directions and generates a plethora of publications. This paper contains a survey of the main…

A fast and weakly stable method for computing the zeros of a particular class of hypergeometric polynomials is presented. The studied hypergeometric polynomials satisfy a higher order differential equation and generalize Laguerre…

We discuss various aspects of representation of a polynomial as a sum of monomials (for example, uniqueness of such representation and related estimations).

The main purpose of this paper is to present the generalization of the inequalities between the modulus of the polar derivative and the polynomial itself, depending on consideration of the zeros inside and outside of a closed disk and the…

We study the conditional distribution of zeros of a Gaussian system of random polynomials (and more generally, holomorphic sections), given that the polynomials or sections vanish at a point p (or a fixed finite set of points). The…

The Boubaker polynomials are investigated in this paper. Using Riordan matrices analysis, a sequence of relations outlining the relations with Chebyshev and Fermat polynomials have been obtained. The obtained expressions are a meaningful…

In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.

Using a variety of matrix techniques, the problem of locating the left eigenvalues of the quaternion companion matrices are investigated in this paper. In a recent paper, Dar et al. [6], proved that the zeros of a quaternionic polynomial…

In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.

We study the twisted q-zeta functions and twisted q-Bernoulli polynomials