An efficient resultant for determining reciprocal zeros in polynomials

Some compact generalization of inequalities for polynomials with prescribed zeros

‎Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$‎, ‎$k^2 leq rRleq R^2$ and for $Rleq r leq k$‎. ‎Our results refine and generalize certain well-known polynomial inequalities‎.

On Zeros of Reciprocal Polynomials of Odd Degree

The first author [1] proved that all zeros of the reciprocal polynomial Pm(z) = m ∑ k=0 Akz k (z ∈ C), of degree m ≥ 2 with real coefficients Ak ∈ R (i.e. Am 6= 0 and Ak = Am−k for all k = 0, . . . , [ m 2 ] ) are on the unit circle, provided that |Am| ≥ m ∑ k=0 |Ak −Am| = m−1 ∑ k=1 |Ak −Am|. Moreover, the zeros of Pm are near to the m + 1st roots of unity (except the root 1). A. Schinzel [3] g...

Research Article On Zeros of Self-Reciprocal Random Algebraic Polynomials

This paper provides an asymptotic estimate for the expected number of level crossings of a trigonometric polynomial TN (θ)= ∑N−1 j=0 {αN− j cos( j +1/2)θ + βN− j sin( j +1/2)θ}, where αj and βj , j = 0,1,2, . . . ,N − 1, are sequences of independent identically distributed normal standard random variables. This type of random polynomial is produced in the study of random algebraic polynomials w...

On the Zeros of a Family of Self-Reciprocal Polynomials

A companion matrix resultant for Bernstein polynomials