On Periodicity of Entire Functions

Chung-Chun Yang
1974 Proceedings of the American Mathematical Society  
A sequence S={sn} is said to be a periodic set of period r (-¿0) if and only if S*={í"+t} can be rearranged to be a sequence to coincide with 5. Let F be the class of all entire functions /satisfying the growth condition: lim sup log log log M(r,f )/\og r < 1. r-»-oo In this paper it is shown that if/e Fand the zero sets of /and /' both are periodic sets with the same period t, then/can be expressed asf(z)=ec'g(z), where c is a constant and^(z) is a periodic entire function with period t. A
more » ... ith period t. A counterexample is exhibited to show that the above condition is a necessary one.
doi:10.2307/2038895 fatcat:2f7763jq2zautnbilstnm43kyy