Asymptotic distribution of zeros of a certain class of hypergeometric polynomials

Abstract

We study the weak asymptotic behavior of the zeros of a family of a certain class of (generalized) hypergeometric polynomials, using the associated hypergeometric differential equation, as the parameters go to infinity. We describe the curve complex on which the zeros cluster, as level curves associated to integrals on an algebraic curve derived from the equation. In a certain degenerate case we make a precise conjecture, based and generalizing work by Duren, Driver et. al, and present experimental evidence for it.