Complex Induction and Heat-Flow Stability of Polynomial Zeros From a Speculative Inductive Principle to a Concrete Cubic Problem

Abstract

This paper records an exploratory mathematical program originating from a proposednotion called complex induction. The original idea was an attempt to formulate an inductiveprinciple for complex functions analogous, in spirit, to ordinary induction over the naturalnumbers. The initial motivation included the possibility of propagating analytic propertiesthrough transformations of functions.The original formulation did not lead directly to a rigorous induction principle. Duringsubsequent exploration, however, the problem was transformed into a concrete questionconcerning the evolution of polynomial zeros under the heat operator