论文标题
三角形组：自动形式和非线性微分方程
Triangle Groups: Automorphic Forms and Nonlinear Differential Equations
论文作者
论文摘要
我们研究了与三角形组相关的准形态形式的关系的关系，从而将我们的早期结果扩展到Hecke组上。与这些三角形组相关的爱森斯坦系列显示出满足拉曼努扬的身份。这些身份反过来允许我们将非线性微分方程与每个三角形组相关联。我们表明，在组作用下，与三角形群及其轨道相关的准形态重量-2 Eisenstein系列解决了它们。我们通过讨论这些非线性微分方程的painlevé特性来结束。
We study the relations governing the ring of quasiautomorphic forms associated to triangle groups with a single cusp, thereby extending our earlier results on Hecke groups. The Eisenstein series associated to these triangle groups are shown to satisfy Ramanujan-like identities. These identities in turn allow us to associate a nonlinear differential equation to each triangle group. We show that they are solved by the quasiautomorphic weight-2 Eisenstein series associated to the triangle group and its orbit under the group action. We conclude by discussing the Painlevé property of these nonlinear differential equations.
