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On the Periodicity of Compositions of Entire Functions. II

Published online by Cambridge University Press:  20 November 2018

Fred Gross
Fred Gross*
Affiliation:
Bellcomm, Inc., Washington, D.C.
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In (1) the author suggested the following research problem. Does there exist a non-periodic entire function ƒ such that ƒƒ is periodic? My aim in this note is to give a partial answer to this question and, more generally, to give a partial solution to the following problem: if ƒ and g are entire functions and ƒ(g) is periodic, what can one say about g? These results also extend a previous result of mine; for details, see (2, Theorem 4). We begin with some simple lemmas.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1265 - 1268
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Gross, Fred, Research problem, On periodic entire functions, Bull. Amer. Math. Soc. 72 1966), 656.Google Scholar
2. Gross, Fred, On the periodicity of compositions ofentire functions, Can. J. Math. 18 (1966), 724–730.Google Scholar
3. Nevanlinna, Rolf, Théorème de Picard Borel, p. 117 (Gauthier-Villars, Paris, 1929).Google Scholar