On the Zeros of Polynomials with Concentration at Low Degrees, II

Let 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.