Entire functions with two radially distributed values

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.

arXiv comment24 pages; correction of one example added in v3

References in corpus (8)

• PT-Symmetric Quantum Mechanics
• The ODE/IM Correspondence
• PT-symmetric quantum mechanics
• On the relation between Stokes multipliers and the T-Q systems of conformal field theory
• The potential (iz)^m generates real eigenvalues only, under symmetric rapid decay conditions
• Goldberg's constants
• Value distribution and potential theory
• Simultaneous stabilization, avoidance and Goldberg's constants

Cited by in corpus (1)

• Radially distributed values and normal families