Automorphic Integral Transforms for Classical Groups I: Endoscopy Correspondences

By Dihua Jiang. 2012

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A general framework of constructions of endoscopy correspondences via automorphic integral transforms for classical groups is formulated in terms of the Arthur classification of the discrete spectrum of square-integrable automorphic forms. This suggests a principle, which is called the $(\tau,b)$-theory of automorphic forms of classical groups, to reorganize and extend the series of work of Piatetski-Shapiro, Rallis, Kudla and others on standard $L$-functions of classical groups and theta correspondence.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/34aa131c7500bf8a5cf917821d817658b045be57