We confirm a conjecture of Marklof regarding the limiting distribution 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 result is then used along the lines suggested by Marklof to give an analogue of a result of Schmidt regarding the distribution of shapes of lattices orthogonal to integer vectors.
Bibliographical noteFunding Information:
M. E. acknowledges support of SNF grant 200021-127145. S. M. acknowledges the support of ISF grant 1003/11, BSF grant 2010295, and the University of Zurich. N. S. acknowledges the support of NSF grant 1001654. Chaya Fellow U. S., acknowledges the partial support of the Advanced Research Grant 228304 from the European Research Council and ISF grant 357/13.
© Foundation Compositio Mathematica 2015.
- Homogeneous spaces
- Shapes of orthogonal lattices