Abstract

Suppose ∑n=0∞anzn has radius of convergence R and σN(z)=|∑n=N∞anzn|. Suppose |z1|<|z2|<R, and T is either z2 or a neighborhood of z2. Put S={N|σN(z1)>σN(z) for zϵT}. Two questions are asked: (a) can S be cofinite? (b) can S be infinite? This paper provides some answers to these questions. The answer to (a) is no, even if T=z2. The answer to (b) is no, for T=z2 if liman=a≠0. Examples show (b) is possible if T=z2 and for T a neighborhood of z2.