General Bilinear Forms In The Jacobi Symbol Over Hyperbolic Regions

Abstract

We study averages involving the Jacobi quadratic symbol $(\frac{n}{m})$ in regions where the product $mn$ is bounded by a large parameter. We show that these averages exhibit cancellation whenever the summation is restricted to square-free integers bounded away from the axes.

arXiv commentAccepted for publication by Monatshefte für Mathematik