Automorphic Forms on Adele Groups. (AM-83), Volume 83 by Stephen S. Gelbart (Paperback, 1975)

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ISBN-13: 9780691081564, 978-0691081564. A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory.

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The subject matter of these Notes is the interplay between the theory of automorphic forms and group representations. One goal is to interpret some recent developments in this area, most significantly the theory of Jacquet-Langlands, working out, whenever possible, explicit consequences and connections with the classical theory. Another goal is to