On Simultaneous Approximation of Algebraic Power Series over a Finite Field

In 1970, W. M. Schmidt [6] generalized Roth’s well-known theorem on rational approximation to a single algebraic irrational, to include simultaneous rational approximation for a given \(n\) algebraic irrationals. As no analogue of Roth’s theorem for algebraic irrational power series over a finite field exists, we will show that there is no analogue of Schmidt’s theorem for such \(n\) elements.