ON THE VALUES OF SOME POWER SERIES IN THE FIELD OF FORMAL LAURENT SERIES OVER A FINITE FIELD

Abstract

In 1932, Mahler introduced a classification of transcendental numbers that pertained to both complex and p-adic numbers. Bundschuh then extended Mahler's classification so that it included the field of formal Laurent series over a finite field. Herein, we show that the values of some power series in field of formal Laurent series over a finite field are either Liouville numbers, or they can be included in the quotient field of the polynomial ring on the finite field for Liouville number arguments under certain conditions.