Graphs of zeros of analytic families

Abstract

Abstract. Let F := {f λ } be a family of holomorphic functions in a domain D ⊂ C depending holomorphically on λ ∈ U ⊂ C n . We study the distribution of zeros of {f λ } in a subdomain R ⊂⊂ D whose boundary is a closed nonsingular analytic curve. As an application, we obtain several results about distributions of zeros of families of generalized exponential polynomials and displacement maps related to certain ODE's.