  We give a local expression for the {\it scalar curvature} of the
noncommutative two torus $ A_{\theta} = C(\mathbb{T}_{\theta}^2)$ equipped with
an arbitrary translation invariant complex structure and Weyl factor. This is
achieved by evaluating the value of the (analytic continuation of the) {\it
spectral zeta functional} $\zeta_a(s): = \text{Trace}(a \triangle^{-s})$ at
$s=0$ as a linear functional in $a \in C^{\infty}(\mathbb{T}_{\theta}^2)$. A
new, purely noncommutative, feature here is the appearance of the {\it modular
automorphism group} from the theory of type III factors and quantum statistical
mechanics in the final formula for the curvature. This formula coincides with
the formula that was recently obtained independently by Connes and Moscovici in
their recent paper.
