Ichiro Amemiya’s scientific contributions

... This question is known as Ozawa's problem. This problem has been answered partly by Amemiya-Ozawa [1] and by Gundersen [8], while the complete solution is given by Langley [22]. It was shown in [22] that if A = ce −z , where c ∈ C \ {0}, and B(z) is a non-constant polynomial, then all non-trivial solutions of (1.3) are infinite order. ...

Reference:

Representation of finite order solutions to linear differential equations with exponential sum coefficients