Let {Pn(z)} be a sequence of polynomials satisfying a linear homogeneous recursion whose coefficients are polynomials in z. Necessary and sufficient conditions are found, subject to mild nondegeneracy conditions, that a number x be a limit of zeroes of {Pn} in the sense that there is a sequence {zn} with Pn(zn) = 0, zn→x. An application is given to a family of polynomials arising in a map-coloring problem.
展开▼
