Correspondences between K3 surfaces

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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 ρ=17 and a Kummer surface having transcendental lattices -Hodge isomorphic.