Entire functions with two radially distributed values
Walter Bergweiler, Alexandre Eremenko, Aimo Hinkkanen
TL;DR
This paper investigates entire functions with zeros and one-points distributed along specific rays, establishing restrictions and constructing examples using differential equation techniques.
Contribution
It introduces new restrictions on the distribution of zeros and one-points on rays and constructs explicit examples via the Stokes phenomenon.
Findings
Restrictions on the rays where zeros and one-points can lie
Construction of entire functions with zeros and one-points on different rays
Application of the Stokes phenomenon to function construction
Abstract
We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are constructed, using the Stokes phenomenon for second order linear differential equations.
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