Maximum Curves of Transcendental Entire Functions of the Form E^{p(z)}

Abstract

The function f(z) = e^{p(z)} where p(z) is a polynomial of degree n has 2n Julia lines. Julia lines of e^{p(z)} divide the complex plane into 2n equal sectors with the same vertex at the origin. In each sector, e^{p(z)} has radial limits of 0 or innity. Main results of the paper are concerned with maximum curves of e^{p(z)}. We deal with some properties of maximum curves of ep^{(z)} and we give some examples of the maximum curves of functions of the form e^{p(z)}.