On the Construction of Continued Fraction Normal Series in Positive Characteristic

Motivated by the famous Champernowne construction of a normal number, R. Adler, M. Keane, and M. Smorodinsky constructed a normal number with respect to the simple continued fraction transformation. In this paper, we follow their idea and construct a normal series for the Artin continued fraction expansion in positive characteristic. A normal series for Ltiroth expansion is also discussed.