International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 1, Pages 29-40
A class of gap series with small growth in the unit disc
Department of Mathematical Sciences, Northern Illinois University, DeKalb 60115, IL, USA
Received 14 November 2001
Copyright © 2002 L. R. Sons and Zhuan Ye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let and let be an integer which is at least
. If is an analytic function in the unit disc which has power series representation
, , then the first author has proved that is unbounded in every sector , for . A natural conjecture concerning these functions is that , where is the minimum of on and is the maximum of on . In this paper, investigations concerning this conjecture
are discussed. For example, we prove that and when .