Exponential sums on reduced residue systems

The aim of this article is to obtain an upper bound for the exponential sums ∑ e(f(x)/q), where the summation runs from x = 1 to x = q with (x, q) = 1 and e(α) denotes exp(2πiα). We shall show that the upper bound depends only on the values of q and s, where s is the number of terms in the polynomial f(x).