Composite polynomials

On an Asymptotical Moments Problem

“…It turns out that, under a specific conditions, the validity of the asymptotic relation (1) for some = m > 1, implies its validity for all moments of lesser order. This result is characterized in the first proposition.…”

On zero-free regions for the derivative of a polynomial

“…Let us suppose that p(z) is an n th degree polynomial which has all its zeros in the unit disk 1  z , then all the critical points of p(z) also lie in the same disk 1  z .This is in fact the wellknown Theorem which was implied in a note of Gauss dated 1836 and proved explicitly by Lucas dated 1874 (see also Marden [1]. Now instead of considering the relative position of all the zeros and critical points of p(z), let us choose any one zero z o of p(z) and ask: At most how far from z o does the nearest critical point lie ?…”

Results on the spectrum of r -modes of slowly rotating, relativistic stars

“…The analysis of the solutions of (60) uses Theorem (39,1) in [31] which generalizes the Routh-Hurwitz theorem to polynomials with complex coefficients. For this solutions with Re(γ) < 0, Re(γ) > 0, will be referred to as 'stable' and 'unstable', respectively.…”