Extending sawtooth functions to Hurwitz polynomials

An extension of the properties of sawtooth functions is applied to rational Hurwitz polynomials of the form H(z)=p(z)/q(z). When H(z) is rational, the functions for p(z) and q(z) are defined in a function f(m± in), where m and n are integers. The integer function describes the slope of a sawtooth with a unity period scanning through a rational point on a unit circle. Roots of H(z) can be found through analysis of the integer function