Geodesic
On the Periodicity of Compositions of Entire Functions. II
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1265-1268

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Gross, Fred. On the Periodicity of Compositions of Entire Functions. II. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1265-1268. doi: 10.4153/CJM-1968-123-4
@article{10_4153_CJM_1968_123_4,
     author = {Gross, Fred},
     title = {On the {Periodicity} of {Compositions} of {Entire} {Functions.} {II}},
     journal = {Canadian journal of mathematics},
     pages = {1265--1268},
     year = {1968},
     volume = {20},
     number = {1},
     doi = {10.4153/CJM-1968-123-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-123-4/}
}
TY  - JOUR
AU  - Gross, Fred
TI  - On the Periodicity of Compositions of Entire Functions. II
JO  - Canadian journal of mathematics
PY  - 1968
SP  - 1265
EP  - 1268
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-123-4/
DO  - 10.4153/CJM-1968-123-4
ID  - 10_4153_CJM_1968_123_4
ER  - 
%0 Journal Article
%A Gross, Fred
%T On the Periodicity of Compositions of Entire Functions. II
%J Canadian journal of mathematics
%D 1968
%P 1265-1268
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-123-4/
%R 10.4153/CJM-1968-123-4
%F 10_4153_CJM_1968_123_4

[1] 1. Gross, Fred, Research problem, On periodic entire functions, Bull. Amer. Math. Soc. 72 1966), 656. Google Scholar

[2] 2. Gross, Fred, On the periodicity of compositions ofentire functions, Can. J. Math. 18 (1966), 724–730. Google Scholar

[3] 3. Nevanlinna, Rolf, Théorème de Picard Borel, p. 117 (Gauthier-Villars, Paris, 1929). Google Scholar

Cité par Sources :