Quantitative arithmetic of diagonal degree 2 K3 surfaces

In this paper we study the existence of rational points for the family of K3 surfaces over Q given by w2=A1x61+A2x62+A3x63. When the coefficients are ordered by height, we show that the Brauer group is almost always trivial, and find the exact order of magnitude of surfaces for which there is a Brauer–Manin obstruction to the Hasse principle. Our results show definitively that K3 surfaces can have a Brauer–Manin obstruction to the Hasse principle that is only explained by odd order torsion