Simultaneous approximation in positive characteristic

Let r = r(alpha) be the approximation exponent of a power series alpha (so that when alpha is algebraic of degree d, then 2 less than or equal to r le ss than or equal to d by Dirichlet's and Liouville's Theorems). If the char acteristic is positive, q is a power of the characteristic, and rr, as are related by a fractional linear transformation with polynomial coefficients, then by respective work of Voloch and of de Mathan, there are constants B- V ,B-M such that \alpha - P/Q\ < B\Q\(-r) has no solution if B < B-V, and i nfinitely many solutions if B > B-M We will formulate acid prove generaliza tions to simultaneous approximation. 2000 Mathematics Subject Classificatio n: 11J61, 11J13.