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Growth of coefficients of universal Taylor series and comparison of two classes of functions. (English) Zbl 0894.30003
In this paper the authors study the order of growth of the coefficients of universal Taylor series and give several theorems. Let \(U\) be the class of universal Taylor series (a sub-class of the Taylor series with complex coefficients that converge within the unit disc). As consequences of the results proved, they show that the class \(U\) is disjoint from the Nevanlinna class and that no universal Taylor series is summable \((C,k)\) at any point \(z\), \(| z|=1\), for any \(k\). Relations between some other associated classes of functions are also studied.

MSC:
30B10 Power series (including lacunary series) in one complex variable
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