Unipotent mixing for general moduli

TL;DR

This paper proves a joint equidistribution result for discrete low lying horocycles, extending previous work by removing the prime number restriction on the discrete points, thus broadening the understanding of unipotent mixing.

Contribution

It generalizes earlier results by establishing equidistribution for non-prime discrete points, advancing the theory of unipotent mixing in moduli spaces.

Findings

Proves joint equidistribution for low lying horocycles

Extends previous results to non-prime discrete points

Broadens applicability of unipotent mixing results

Abstract

In this note we prove a joint equidistribution result for discrete low lying horocycles. This generalizes previous work of Blomer and Michel, where it was crucially assumed that the number of discrete points is prime.