motivated by questions in pointwise ergodic theory, modern discrete harmonic analysis, as developed by bourgain, has focused on understanding the oscillation of averaging operators -- or related singular integral operators -- along polynomial curves. in this talk we present the first example of a discrete analogue of polynomially modulated oscillatory singular integrals; this begins to unify the work of bourgain, stein, and stein-wainger. the argument combines a wide range of techniques from euclidean harmonic analysis and analytic number theory.