Automorphic Integral Transforms for Classical Groups I: Endoscopy Correspondences

Abstract

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.

80 pages, submitted to the proceedings of the conference: Automorphic Forms and Related Geometry: assessing the legacy of I.I. Piatetski-Shapiro