2 problems

Let $l\geq 1$ be an integer, and let $(H_l/\Gamma,g)$ be a rational $(2l+1)$-dimensional Heisenberg manifold. Let $N(t)$ be its spectral counting function and let $R(t)$ denote the…

Let $(\Gamma\backslash H_1,g)$ be a three-dimensional Heisenberg manifold with a left-invariant metric, and let $R(t)$ denote the remainder term in Weyl's law. For $\delta>0$, writ…