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The existence of $T$-numbers in positive characteristic

Volume 189 / 2019

Tomohiro Ooto Acta Arithmetica 189 (2019), 179-189 MSC: Primary 11J82; Secondary 11J61. DOI: 10.4064/aa180325-24-8 Published online: 17 May 2019


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.


  • Tomohiro OotoFaculty of Pure and Applied Sciences
    University of Tsukuba
    Tennodai 1-1-1
    Tsukuba, Ibaraki, 305-8571, Japan

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