Computational Methods and Function Theory 7 (2007), No. 2, 563--571
Copyright Heldermann Verlag 2007
Janis Meyer
pmzjm2@maths.nott.ac.uk , University of Nottingham, School of Mathematical Sciences, Nottingham, NG7 2RD, U.K.
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 (zn) 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 (zn). This result supports a conjecture of D. Drasin and J. Langley.
Keywords: Bank-Laine functions, regularly distributed zeros, growth of entire functions.
MSC 2000: 30D35, 34M10.
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