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 L\"uroth expansion is also discussed.