The limit distribution of primitive rational points on expanding horospheres on SL(n,Z)/SL(n, R) has been derived in the recent work by M. Einsiedler, S. Mozes, N. Shah and U. Shapira. For n=3, in our joint project with Jens Marklof, we prove the effective equidistribution of q-primitive points on expanding horospheres as q→∞.
Our proof relies on Fourier analysis and Weil's bound on Kloosterman sums. We will also discuss applications in number theory.