In this paper, using the Weierstrass–Enneper formula and the hodographic coordinate system, we find the relationships between the Ramanujan identity and a generalized class of minimal translation surfaces, known as affine minimal translation 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 remark the analogous forms in \({\mathbb {L}}^3.\)

中文翻译：

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关于仿射最小平移曲面和拉马努金恒等式

在本文中，使用 Weierstrass-Enneper 公式和全息坐标系，我们找到了 Ramanujan 恒等式与广义类最小平移曲面（称为仿射最小平移曲面）之间的关系。我们发现仿射 Scherk表面的 Dirichlet 级数展开。我们还获得了仿射 Scherk表面关于其对数分布的一些概率度量。接下来，我们在仿射最小翻译表面分类\（{\ mathbb {L}} ^ 3 \）和备注在类似形式\（{\ mathbb {L}} ^ 3 \）