The simultaneous diophantine approximation of values of functions satisfying certain n variable q-difference equations

In a previous paper lower bounds were obtained on the simultaneous diophantine approximation of values of certain functions which satisfy linear q-difference equations. In the present paper these results are generalized from n = 1 to n > 1 variables. In order to better see what some of these solutions “look like” the algebraic properties of certain classes of functions are investigated, particularly with regard to a type of multiplication which is analogous to the convolution product. At the end of the paper such algebraic results are also obtained for the case n = 1.