Smooth-automorphic forms and smooth-automorphic representations
Author(s)
Bibliographic Information
Smooth-automorphic forms and smooth-automorphic representations
（Series on number theory and its applications / series editor, Shigeru Kanemitsu, v. 17）
World Scientific, c2023
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Note
Includes bibliographical references (p. 231-239) and index
Description and Table of Contents
Description
This book provides a conceptual introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F.Our approach to automorphic representations differs from the usual literature: We do not consider 'K-finite' automorphic forms, but we allow a richer class of smooth functions of uniform moderate growth. Contrasting the usual approach, our space of 'smooth-automorphic forms' is intrinsic to the group scheme G/F.This setup also covers the advantage that a perfect representation-theoretical symmetry between the archimedean and non-archimedean places of the number field F is regained, by making the bigger space of smooth-automorphic forms into a proper, continuous representation of the full group of adelic points of G.Graduate students and researchers will find the covered topics appear for the first time in a book, where the theory of smooth-automorphic representations is robustly developed and presented in great detail.
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