Abstract
We show that exponential growth is the critical discrete rate of growth for zero-free entire functions which are universal in the sense of MacLane. Specifically, it is proved that, if the lower exponential growth order of a zero-free entire function f is finite, then f cannot be hypercyclic for the derivative operator; and, if a positive function φ having infinite exponential growth is fixed, then there exist zero-free hypercyclic functions which are controlled by φ along a sequence of radii tending to infinity.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
