The asymptotic distribution of exponential sums, II

Let f(x) be a polynomial with integral coefficients and let, for c > 0, S(f(x),c) = Sigma i ((mod) (C)) exp(2 pi i f(i)/c). If f is a cu-c polynomial then it is expected that Sigma c <= xS(f(x), c) similar to k (f)(f)X-4/3. In this paper, we consider the special case f(x) =Ax(3) + Bx and propose a precise formula for k(f). This conjecture represents a refined version of the classical Kummer conjecture.