Primitive rational points on expanding horospheres in Hilbert modular surfaces

Abstract

In recent work by Einsiedler, Mozes, Shah and Shapira the limiting distributions of primitive rational points on expanding horospheres was examined in arbitrary dimension, and a suspended version of this result was announced. Motivated by this, we prove an analog to the announcement for primitive rational points in Hilbert modular surfaces via effective mixing.

Corrections to Propositions 3.5 and 3.6. General improvements on exposition and notation