Spectral asymptotics of sub-Riemannian Laplacians on compact Heisenberg manifolds

Let \(N_M(λ)\) be the spectral counting function of the sub-Laplacian on the compact Heisenberg manifold \(M=Γ\backslash\mathbb H_d\), where $Γ$ is a lattice subgroup of the Heisenberg group $\mathbb H_d$. In 2016, Strichartz \cite[\textit{J. Geom. Anal.}]{Str16} proved the Weyl law with remainder \