On Bank-Laine type functions

Abstract

We continue our previous study on the Bank-Laine type functions: meromorphic functions f that satisfy f(z) = 0 ⇐⇒ f ' (z) ∈ {a;b} on the plane, where a;b are two distinct nonzero values. Using quasi-normality, we prove that there is no transcendental meromorphic function with this property when the quotient a=b is a positive integer. Moreover, we prove a quasi-normal criterion for families of such functions. This completes our previous results.