Equidistribution of continuous low-lying pairs of horocycles via Ratner's theorem

TL;DR

This paper presents an alternative proof for a joint equidistribution result of low-lying horocycles, utilizing Ratner's theorem, which extends the result to non-uniform lattices, offering broader applicability.

Contribution

The paper introduces a new proof method based on Ratner's theorem, extending equidistribution results to non-uniform lattices.

Findings

Alternative proof of joint equidistribution using Ratner's theorem

Extension of equidistribution results to non-uniform lattices

Simplification of previous proofs with broader applicability

Abstract

We record an alternative proof of a recent joint equidistribution result of Blomer and Michel, based on Ratner's topological rigidity theorem. This approach has the advantage of extending to non-uniform lattices.