**Title**: Primitive rational points on expanding horospheres

**Speaker**: Manuel Luethi (ETH-Zurich)

**Abstract**: An observation by Marklof implies that the primitive rational points of denominator n along the stable horocycle orbits of large volume determined by n equidistribute within a proper submanifold of the unit tangent bundle to the modular surface. We examine the general behavior of primitive rational points along expanding horospheres and prove joint equidistribution in products of the torus and the unit tangent bundle to the modular surface using effective mixing for congruence quotients.