The existence of $T$-numbers in positive characteristic

Abstract

As an analogue of Mahler's classification for real numbers, Bundschuh introduced a classification for Laurent series over a finite field, divided into $A,S,T,U$-numbers.It is known that each of $A,S,U$-numbers is nonempty.On the other hand, the existence of $T$-numbers is open.In this paper, we give an affirmative answer to the problem.