A quantitative Khintchine-Groshev type theorem over a field of formal series

An asymptotic formula which holds almost everywhere is obtained for the number of solutions to theDiophantine inequalities ‖qA − p‖ < Ψ(‖g‖), where A is an n x m matrix (m > 1) over the field of formal Laurent series with coefficients from a finite field, and p and q are vectors of polynomials over the same finite field.