On modular counting with polynomials

For any integers m and l, where m has r sufficiently large (depending on l) factors, that are powers of r distinct primes, we give a construction of a (symmetric) polynomial over Z_m of degree O(^rradicn) that is a generalized representation (commonly also called weak representation) of the MOD_l function. We give a detailed study of the case when m has exactly two distinct prime factors, and classify the minimum possible degree for a symmetric representing polynomial