Analytic Aspects of L-functions and Related Problems

本文主要研究自同构l函数解析问题的新方法，以及它们与数论中各种等分布问题的内在联系，特别是算术曲面上Hecke特征形式的质量等分布性质的定量和有效结果，以及它的高维推广。等分布问题起源于数学物理和量子力学，并与数学的其他主要领域密切相关。不同领域的想法之间丰富的相互作用和互动是当前项目的核心。由于这些独特的特点，这里提出的研究项目也非常适合在一个充满活力和重要的研究领域培养和吸引博士后研究人员和博士生。

This proposal is centered on new approaches to tackle problems concerning analytic aspects of automorphic L-functions, and their intrinsic connnection to various equidistribution problems in Number Theory, especially the quantitative and effective results in the mass equidistribution properties of Hecke eigenforms on arithmetic surfaces, as well as its higher dimensional generalizations. The equidistribution problems have their origin from mathematical physics and quantum mechanics, and are well connected to other major areas in mathematics. The rich interplay and interaction of ideas across different fields lie at the heart of the current project.Because of these distinctive features the research project proposed here are also ideal for training and engaging postdoctoral researchers and Ph.D. students in a vibrant and important research area.