Fourier Coefficients, L-functions, and Endoscopy Correspondences of Automorphic Forms

PI, Dihua Jiang，研究了自同构l函数和可积自同构形式的显式Langlands泛函转移的一些基本问题。他研究了自同构形式的离散谱的基本结构和朗兰兹泛函的相关问题。在局部理论方面，他的研究攻击了p进群调和分析中的局部朗兰兹猜想和相关的基本问题。他的长期目标是了解自同构形式理论中的一般局部-全局自同构原理，它反映了算术和数论的基本原理之一。PI蒋迪华是自同态形式的现代理论和朗兰兹纲领方面的专家。自同构形式是具有丰富对称性的函数。这些对称性是我们理解宇宙中物体内在结构的指南。在数学中，这些对称性是许多不同理论的共同基础，如几何、数论、数学物理、代数和分析。因此，自同构形式的现代理论，本质上是朗兰兹纲领，为这些领域的进一步研究提供了组织原则。蒋迪华的研究建立了自同构形式的基本结构，因此对朗兰兹纲领做出了重要贡献。

The PI, Dihua Jiang, has been working on some basic problems related to Automorphic L-functions and explicit Langlands functorial transfers for square-integrable automorphic forms. He investigates the basic structures of the discrete spectrum of automorphic forms and the related problems on the Langlands functoriality. In the local theory, his research attacks the local Langlands conjectures and related basic problems in harmonic analysis of p-adic groups. His long term goal is to understand the general local-global-automorphic principles in the theory of automorphic forms, which reflects one of the basic principles in the arithmetic and number theory.The PI, Dihua Jiang, is an expert in the modern theory of automorphic forms and the Langlands Program. Automorphic forms are functions with abundant symmetries. These symmetries are the guidelines to understand the intrinsic structures of objects in our universe. In Mathematics, these symmetries are common grounds for many different theories such as Geometry, Number Theory, Mathematical Physics, Algebra and Analysis. Hence the modern theory of automorphic forms, essentially the Langlands program, provides the organizing principle for further research in these areas. The research of Dihua Jiang establishes basic structures for automorphic forms and hence yields essential contribution to the Langlands program.