EUGÈNE DUBOIS
In 1932, K. Mahler introduced his famous classification for complex numbers in disjoint sets A, S, T, U [9, 10]. In 1978, P. Bundschuh introduced a similar classification for the field of formal Laurent series over a finite field K and gave some explicit series in the class U. Here we consider the case of an arbitrary field K and prove the existence of U-numbers whose continued fractions verify additional properties.