The existence of $T$-numbers in positive characteristic
Volume 189 / 2019
Acta Arithmetica 189 (2019), 179-189
MSC: Primary 11J82; Secondary 11J61.
DOI: 10.4064/aa180325-24-8
Published online: 17 May 2019
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 the sets of $A,S,U$-numbers is nonempty. On the other hand, the existence of $T$-numbers has been an open problem. In this paper, we prove that they exist.
