Correspondences between K3 surfaces

In this paper we show that there is a correspondence between some $K3$ surfaces with non-isometric transcendental lattices constructed as a twist of the transcendental lattice of the Jacobian of a generic genus 2 curve. Moreover, we show the existence of a correspondence between a general $K3$ surface with $\rho =17$ and a Kummer surface having transcendental lattices $\QQ$-Hodge isomorphic.