Hyperbolic polynomials and rigid orders of moduli. (English) Zbl 1524.26022
Summary: We prove that the order of the absolute values of the zeros of a hyperbolic polynomial, with at least one negative and one positive zero, determines the signs of its coefficients if and only if the moduli of the positive and negative zeros interlace.
MSC:
| 26C10 | Real polynomials: location of zeros |
| 30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |
