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

作者蒋迪华一直致力于研究平方可积自同构形式的L函数和显式朗兰兹函数变换的一些基本问题。他研究了自同构型的离散谱的基本结构以及与朗兰兹函数有关的问题。在局域理论中，他的研究攻击了局域朗兰兹猜想和p-Add群调和分析中的相关基本问题。他的长期目标是理解自同构形式理论中的一般局部-全局-自同构原理，这反映了算术和数论中的基本原理之一。皮迪华·江是现代自同构形式理论和朗兰兹计划的专家。自同构型是具有丰富对称性的函数。这些对称性是理解我们宇宙中物体的内在结构的指导方针。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，现代的自同构形式理论，主要是朗兰兹计划，为这些领域的进一步研究提供了组织原则。狄华江的研究建立了自同构形式的基本结构，从而为朗兰兹计划做出了重要贡献。

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.