A class of gap series with small growth in the unit disc
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 .
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