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arXiv 1906.01067math.DSmath.NTmath.SP
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测地线的动力学和马斯尖点形式

Dynamics of geodesics, and Maass cusp forms

A. Pohl, D. Zagier

摘要:

量子力学与经典力学之间的对应原理揭示了黎曼流形的谱实体与几何实体之间的深刻联系。我们调查-在某种程度上旨在访问广大观众的数学家-数学上严格的例子,这种关系出现在最近几年,显示了动力学解释某些拉普拉斯特征函数的双曲曲面。

英文摘要:

The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide audience of mathematicians---a mathematically rigorous instance of such a relation that emerged in recent years, showing a dynamical interpretation of certain Laplace eigenfunctions of hyperbolic surfaces.

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