On modular counting with polynomials

Abstract

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 Zm of degree O(rradicn) that is a generalized representation (commonly also called weak representation) of the MODl 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