Limits of zeroes of recursively defined polynomials.
Let {P(n)(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 {P(n)} in the sense that there is a sequence {z(n)} with P(n)(z(n)) = 0, z(n)-->x. An application is given to a family of polynomials arising in a map-coloring problem.
Beraha
S
S
Department of Mathematics, Queens College, City University of New York, Flushing, New York 11367.
Kahane
J
J
Weiss
N J
NJ