# A short proof of sharp Weyl's law for the special orthogonal group

## TL;DR

This paper provides a concise proof of a precise version of Weyl's law for the special orthogonal group, utilizing modular forms, and improves error estimates especially for groups of smaller rank.

## Contribution

It introduces a short proof of Weyl's law for SO(N) leveraging modular forms and refines error bounds for lower ranks.

## Key findings

- Error term exponent is sharp for rank ≥ 4
- Improved results for smaller rank cases
- Utilizes well-known modular form theory

## Abstract

We give a short proof of a strong form of Weyl's law for $\text{SO}(N)$ using well known facts of the theory of modular forms. The exponent of the error term is sharp when the rank is at least~$4$. We also discuss the cases with smaller rank improving previous results.