Abstract:

This paper mainly learned classic book `Nevanlinna theory and complex differential equations' due to Laine and considered the second order complex differential equation $f ''(z) + A (z) f(z)=0, \lambda(f)<\infty$ with coefficient $A (z) $ whose period is $2 \pi{\rm i}$. It found a possible error in the original proof and gave its partial correction, and also it gave a slightly weaker conclusion than its possibly controversial result in the original literature.

Key words: Complex differential equation, Nevanlinna theory, Entire function, Exponent of convergence for zero-sequence