On a quaternionic Picard theorem

Abstract

The classical theorem of Picard states that a non-constant holomorphic function $f:\mathbb{C}\to \mathbb{C}$ can avoid at most one value. We investigate how many values a non-constant slice regular function of a quaternionic variable $f:\mathbb{H}\to \mathbb{H}$ may avoid.

15 pages. To appear on Proc. Americ. Math. Soc. (2020)