特殊Riemann Surfaces上Laplacian算子作用于零度丛的本征函数
Eigenfunctions of the Laplacian Acting on Degree Zero Bundles over Special Riemann Surfaces
摘要：
我们发现一个无限集的拉普拉斯算子的本征函数相对于一个平坦的度量与锥形奇点和作用于度零丛的特殊黎曼曲面的亏格大于一。这些特殊的表面对应的黎曼周期矩阵满足一组方程，导致一些理论问题。事实证明，这些表面精确地对应于环面的分支覆盖。这反映在具有特定类型的复乘的雅可比矩阵中。
英文摘要：
We find an infinite set of eigenfunctions for the Laplacian with respect to a flat metric with conical singularities and acting on degree zero bundles over special Riemann surfaces of genus greater than one. These special surfaces correspond to Riemann period matrices satisfying a set of equations which lead to a number theoretical problem. It turns out that these surfaces precisely correspond to branched covering of the torus. This reflects in a Jacobian with a particular kind of complex multiplication.
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