AbstractLet P be a polynomial with concentration d at degree k, with zeros written in increasing order of moduli: 0 ≤ |z1| ≤ |z2| ≤ ··· . We show that the quantity |∑j < k is bounded from above by a number depending only on d and k, for which we give numerical estimates. More precise ones are obtained for Hurwitz polynomials. We finally show that the theory built for Hurwitz polynomials can be extended to a class of entire functions
In this paper, we evaluate the quality of zero bounds on the moduli of univariate complex polynomial...
AbstractWe define a region Hα,ƒ in the complex number field, where α is a complex number, ƒ(x) ϵ K [...
Abstract. In this paper, we put restrictions on the coefficients of polynomials and give bounds conc...
AbstractLet P be a polynomial with concentration d at degree k, with zeros written in increasing ord...
AbstractWe investigate the roots of polynomials with concentration at low degrees, and prove that th...
Polynomials pervade mathematics and much that is beautiful in mathematics is related to polynomials,...
Dissertation is written in 60 pages and is divided into next parts: 1. Preface (pages 2-7) 2. Introd...
AbstractIn this paper we obtain some lower bounds of the integral ∫02π⋯∫02πlog|P(eiθ1,…,eiθn)|dθ12π⋯...
If p(z)=∑nv=0 avzv is a polynomial of degree n, having all its zeros in |z | ≤ 1, then it was prove...
AbstractWe investigate the roots of polynomials with concentration at low degrees, and prove that th...
AbstractA real polynomial is called Hurwitz (stable) if all its zeros have negative real parts. For ...
We put restrictions on the coefficients of polynomials and give bounds concerning the number of zero...
We impose a monotonicity condition with several reversals on the moduli of the coefficients of a pol...
AbstractIf P(z)=∑ν=0ncνzν is a polynomial of degree n having no zeros in |z|<1, then for |β|⩽1, it w...
AbstractLet p(z) = ∑nv = 0avzv be a polynomial of degree at most n vanishing at z = ζ(ζn + 1 ≠ 1). I...
In this paper, we evaluate the quality of zero bounds on the moduli of univariate complex polynomial...
AbstractWe define a region Hα,ƒ in the complex number field, where α is a complex number, ƒ(x) ϵ K [...
Abstract. In this paper, we put restrictions on the coefficients of polynomials and give bounds conc...
AbstractLet P be a polynomial with concentration d at degree k, with zeros written in increasing ord...
AbstractWe investigate the roots of polynomials with concentration at low degrees, and prove that th...
Polynomials pervade mathematics and much that is beautiful in mathematics is related to polynomials,...
Dissertation is written in 60 pages and is divided into next parts: 1. Preface (pages 2-7) 2. Introd...
AbstractIn this paper we obtain some lower bounds of the integral ∫02π⋯∫02πlog|P(eiθ1,…,eiθn)|dθ12π⋯...
If p(z)=∑nv=0 avzv is a polynomial of degree n, having all its zeros in |z | ≤ 1, then it was prove...
AbstractWe investigate the roots of polynomials with concentration at low degrees, and prove that th...
AbstractA real polynomial is called Hurwitz (stable) if all its zeros have negative real parts. For ...
We put restrictions on the coefficients of polynomials and give bounds concerning the number of zero...
We impose a monotonicity condition with several reversals on the moduli of the coefficients of a pol...
AbstractIf P(z)=∑ν=0ncνzν is a polynomial of degree n having no zeros in |z|<1, then for |β|⩽1, it w...
AbstractLet p(z) = ∑nv = 0avzv be a polynomial of degree at most n vanishing at z = ζ(ζn + 1 ≠ 1). I...
In this paper, we evaluate the quality of zero bounds on the moduli of univariate complex polynomial...
AbstractWe define a region Hα,ƒ in the complex number field, where α is a complex number, ƒ(x) ϵ K [...
Abstract. In this paper, we put restrictions on the coefficients of polynomials and give bounds conc...