  In this paper, using the Weierstrass-Enneper formula and the hodographic
coordinate system, we find the relationships between the Ramanujan identity and
the generalized class of Scherk surfaces known as affine Scherk surfaces. We
find the Dirichlet series expansion of the affine Scherk surface. We also
obtain some of the probability measures of affine Scherk surface with respect
to its logarithmic distribution. Next, we classify the affine minimal
translation surfaces in $\mathbb{L}^3$ and remarked the analogous forms in
$\mathbb{L}^3.$
