# Primitive rational points on expanding horospheres in Hilbert modular surfaces

## TL;DR

This paper proves a result about the distribution of primitive rational points on expanding horospheres in Hilbert modular surfaces, extending previous work on limiting distributions in higher dimensions.

## Contribution

It establishes an analog for Hilbert modular surfaces using effective mixing, advancing understanding of rational point distributions in this setting.

## Key findings

- Proves distribution results for primitive rational points in Hilbert modular surfaces.
- Utilizes effective mixing techniques to achieve the results.
- Extends previous higher-dimensional distribution theorems to a specific surface case.

## 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.