We study asymptotic clustering of zeros of random polynomials, and show that the expected discrepancy of roots of a polynomial of degree n, with not necessarily independent coefficients, decays like √ logn/n. Our proofs rely on discrepancy results for deterministic polynomials, and order statistics of a random variable. We also consider the expected number of zeros lying in certain subsets of t...

We study asymptotic clustering of zeros of random polynomials, and show that the expected discrepancy of roots of a polynomial of degree n, with not necessarily independent coefficients, decays like √ logn/n. Our proofs rely on discrepancy results for deterministic polynomials, and order statistics of a random variable. We also consider the expected number of zeros lying in certain subsets of t...

Marcellan, F. and E. Godoy, Orthogonal polynomials on the unit circle: distribution of zeros, Journal of Computational and Applied Mathematics 37 (1991) 195-208. In this paper we summarize some results concerning zeros of orthogonal polynomials with respect to an indefinite inner product. We analyze the inverse problem, i.e., a discrete representation for the functional in terms of the n th ort...

Abstract Inspired by a problem found in textbook of Faddeev and Sominsky we propose new form roots an arbitrary complex number. Our idea uses the zeros some polynomials connected with modified Chebyshev polynomials.

In this paper, the polynomials Pa(x) = x 2l+1 + x + a with a ∈ GF(2) are studied. New criteria for the number of zeros of Pa(x) in GF(2 ) are proved. In particular, a criterion for Pa(x) to have exactly one zero in GF(2 ) when gcd(l, k) = 1 is formulated in terms of the values of permutation polynomials introduced by Dobbertin. We also study the affine polynomial a l x 2l +x l + ax+ 1 which is ...

In this paper, we present a formula for computing the Tutte polynomial of the signed graph formed from a labeled graph by edge replacements in terms of the chain polynomial of the labeled graph. Then we define a family of ‘ring of tangles’ links and consider zeros of their Jones polynomials. By applying the formula obtained, Beraha-Kahane-Weiss’s theorem and Sokal’s lemma, we prove that zeros o...