Exponential lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields

A depth 3 arithmetic circuit can be viewed as a sum of products of linear functions. We prove an exponential complexity lower bound on depth 3 arithmetic circuits computing some natural symmetric functions over a finite field F. Also, we study the complexity of the functions f : D-n --> F for subsets D subset of F, In particular, we prove an exponential lower bound on the complexity of depth 3 arithmetic circuits computing some explicit functions f: (F*)(n) --> F (in particular, the determinant of a matrix).