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

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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.