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Distribution of Shapes of orthogonal Lattices (1609.03070v1)
Published 10 Sep 2016 in math.DS and math.NT
Abstract: It was recently shown by Aka, Einsiedler and Shapira that if d>2, the set of primitive vectors on large spheres when projected to the d-1-dimensional sphere coupled with the shape of the lattice in their orthogonal complement equidistribute in the product space of the sphere with the space of shapes of d-1-dimensional lattices. Specifically, for d=3,4,5 some congruence conditions are assumed. By using recent advances in the theory of unipotent flows, we effectivize the dynamical proof to remove those conditions for d=4,5. It also follows that equidistribution takes place with a polynomial error term with respect to the length of the primitive points.