School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
Abstract:
A Bank-Laine function is an entire function satisfying at every zero of . We determine all Bank-Laine functions of form , with entire. Further, we prove that if is a transcendental entire function of finite order, then there exists a path tending to infinity on which and all its derivatives tend to infinity, thus establishing for finite order a conjecture of Rubel.