Dickson Polynomials that are Permutations

2000 Mathematics Subject Classification: 11T06, 13P10.

On Optimal Quadratic Lagrange Interpolation: Extremal Node Systems with Minimal Lebesgue Constant via Symbolic Computation

ACM Computing Classification System (1998): G.1.1, G.1.2.

Lp extremal polynomials. Results and perspectives

2000 Mathematics Subject Classification: 30C40, 30D50, 30E10, 30E15, 42C05.

On some Extremal Problems of Landau

2000 Mathematics Subject Classification: Primary: 42A05. Secondary: 42A82, 11N05.

Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5

∗ Research partially supported by INTAS grant 97-1644

Generalization of a Conjecture in the Geometry of Polynomials

In this paper we survey work on and around the following conjecture, which was first stated about 45 years ago: If all the zeros of an algebraic polynomial p (of degree n ≥ 2) lie in a disk with radius r, then, for each zero z1 of p, the disk with center z1 and radius r contains at least one zero of the derivative p′ . Until now, this conjecture has been proved for n ≤ 8 only. We also put the conjecture in a more general framework involving higher order derivatives and sets defined by the zeros of the polynomials.

On Representations of Algebraic Polynomials by Superpositions of Plane Waves

* The author was supported by NSF Grant No. DMS 9706883.

Quadratic Mean Radius of a Polynomial in C(Z)

* Dedicated to the memory of Prof. N. Obreshkoff

Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90

Rolle's Theorem for Complex Polynomials with Real Coefficients

Let p(z) be an algebraic polynomial of degree n ¸ 2 with real coefficients and p(i) = p(¡i). According to Grace-Heawood Theorem, at least one zero of the derivative p0(z) is on the disk with center in the origin and radius cot(¼=n). In this paper is found the smallest domain containing at leas one zero of the derivative p0(z).

On Arrangements of Real Roots of a Real Polynomial and Its Derivatives

2000 Mathematics Subject Classification: 12D10.

Overdetermined Strata in General Families of Polynomials

2000 Mathematics Subject Classification: 12D10.

On the Factorization of the Poincaré Polynomial: A Survey

2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.

On Root Arrangements of Polynomial-Like Functions and their Derivatives

2000 Mathematics Subject Classification: 12D10.

A Geometrical Construction for the Polynomial Invariants of some Reflection Groups

2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.