Title

Non-real Zeros of Derivatives of a Class of Real Entire Functions

Faculty Mentor(s)

Dr. Stephanie Edwards, Hope College
Jennifer Halfpap, Hope College

Document Type

Poster

Publication Date

4-15-2011

Abstract

In 1943, G. Polya conjectured that the number of non-real zeros the kth derivative of a real entire function of order greater than 2, with finitely many non-real zeros, tends to infinity as k goes to infinity. This was verified in 2005 by A. Eremenko and W. Bergweiler. A natural extension is whether the number of non-real zeros of the kth derivative increases monotonically as k goes to infinity. We show that the number of non-real zeros of the kth derivative of a function f increases monotonically with differentiation when f(z)=z^me^{K(z)} where m is a natural number and K is in one of several special classes of real polynomials.

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