Quadratic residue patterns and point counting on K3 surfaces

Abstract

Quadratic residue patterns modulo a prime are studied since 19th century. We state the last unpublished result of Lydia Goncharova, reformulate it and prior results in terms of algebraic geometry, and prove it. The core of this theorem is an unexpected relation between the number of points on a K3 surface and that on a CM elliptic curve.