Abstract
A Bank-Laine function is an entire function E such that E(z) = 0 implies that E′(z) = ±1. Such functions arise as products of linearly independent solutions of certain ordinary differential equations. We investigate the extent to which the growth of E can be related with the exponent of convergence of its zeros. We show that if a sequence (z n) is of finite order λ, where λ = (2l + 1)/2, l ∈ ℕ and is regularly distributed on a single ray then there does not exist a Bank-Laine function of finite order having precisely the zero sequence (z n). This result supports a conjecture of D. Drasin and J. Langley.
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