Equidistribution of primitive rational points on expanding horospheres

Abstract

We confirm a conjecture of Jens Marklof regarding the equidistribution of certain sparse collections of points on expanding horospheres. These collections are obtained by intersecting the expanded horosphere with a certain manifold of complementary dimension and turns out to be of arithmetic nature. This equidistribution result is then used along the lines suggested by Marklof to give an analogue of a result of W. Schmidt regarding the distribution of shapes of lattices orthogonal to integer vectors.

Revised version. To appear in Compositio

Cited by in corpus (6)

• Integer points and their orthogonal lattices
• Distribution of Shapes of orthogonal Lattices
• Integer points on spheres and their orthogonal grids
• Primitive rational points on expanding horocycles in products of the modular surface with the torus
• Translates of rational points along expanding closed horocycles on the modular surface
• Matrix Kloosterman sums