Let $\zeta(M,s)$ be the Minakshisundaram-Pleijel zeta function. Where can I find a proof or reference of the following identity? If $M$ is a surface: $$\zeta'(\Delta, 0) = \frac{1}{12}\int_M K dA$$

Where $K $ is the Gaussian Curvature.

Let $\zeta(M,s)$ be the Minakshisundaram-Pleijel zeta function, which encodes the eigenvalues of the Laplace-Beltrami operator. Where can I find a proof or reference of the following identity? If $M$ is a surface: $$\zeta'(\Delta, 0) = \frac{1}{12}\int_M K dA$$

Where $K $ is the Gaussian Curvature.