Families of L-functions and Applications

研究者将继续他对l函数的研究。特别是一般自同构l函数的“次凸”估计问题。它们广泛应用于数论中的经典问题（例如希尔伯特关于用二次型表示数域中的整数的第11个问题）和算术曲面上的特征函数。l函数族和与之相关的对称性的使用是至关重要的。这个项目是关于被称为zeta函数的数学对象的研究。它们编码了算术和几何的深层信息，这些信息存在于它们的定义中。理解这些函数对整数（和素数）理论有着深远的应用，更令人惊讶的是，对量子理论的一些基础问题也有着深远的应用。

The investigator will continue his study of L-functions. Specifically the problem of a 'subconvex' estimate for general automorphic L-functions. These have wide applications to classical problems in number theory (e.g. Hilbert's 11-th problem on representing integers in a number field by a quadratic form) and to eigenfunctions on arithmetic surfaces. The use of the families of L-functions and symmetries associated with them is crucial. This project is concerned with the study of mathematical objects called zeta functions. They encode deep information about the arithmetic and geometry which lie at their definition. Understanding the functions has far reaching applications to the theory of whole numbers (and prime numbers) and more surprisingly to some foundational problems in quantum theory.