Bank-Laine functions with sparse zeros
Bank-Laine functions with sparse zeros
A Bank-Laine function is an entire function $E$ satisfying $E'(z) = \pm 1$ at every zero of $E$. We construct a Bank-Laine function of finite order with arbitrarily sparse zero-sequence. On the other hand, we show that a real sequence of at most order 1, convergence class, cannot be the …