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We use classical methods from analytic number theory to resolve the latticepoint counting problem on the first Heisenberg group, in the case where thegauge function is taken to be the Cygan-Kor$\acute{a}$nyi Heisenberg-norm$\mathcal{N}_{4,1}(z,w)=(|z|^{4}+w^{2})^{1/4}$. In this case, our main theoremestablishes the estimate $\mathcal{E}(x)=\Omega_{\pm}(x^{\frac{1}{2}})$, where$\mathcal{E}(x)=\mathcal{S}(x)-\frac{\pi^{2}}{2}x$ is the error term arising inthe lattice point counting problem, $\mathcal{S}(x)$ is given by$$\mathcal{S}(x)=\sum_{0\leq m^2+n^2<\, x}r_2(m)$$ and$r_2(m)=|\{a,b\in\mathbb{Z}:\,a^{2}+b^{2}=m\}|$ is the familiar sum of squaresfunction. As a corollary, we deduce that the exponent $\frac{1}{2}$ in theupper-bound $\left|\mathcal{E}(x)\right|\ll x^{\frac{1}{2}}\log{x}$ obtained byGarg, Nevo & Taylor can not be improved and is thus best possible, therebyresolving the lattice point counting problem for the case in hand.

On the best possible exponent for the error term in the lattice point counting problem on the first Heisenberg group