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

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Gelbart, Stephen S.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2016]; ©1975
• Year of Publication: 2016
• Language: English
• Series: Annals of Mathematics Studies ; 83
• Physical Description: 1 online resource (227 p.)
• Other title: Frontmatter --; PREFACE --; CONTENTS --; §1. THE CLASSICAL THEORY --; §2. AUTOMORPHIC FORMS AND THE DECOMPOSITION OF L2(ΓSL(2,ℝ)) --; §3. AUTOMORPHIC FORMS AS FUNCTIONS ON THE ADELE GROUP OF GL(2) --; §4. THE REPRESENTATIONS OF GL(2) OVER LOCAL AND GLOBAL FIELDS --; §5 . CUSP FORMS AND REPRESENTATIONS OF THE ADELE GROUP OF GL(2) --; §6. HECKE THEORY FOR GL(2) --; §7 . THE CONSTRUCTION OF A SPECIAL CLASS OF AUTOMORPHIC FORMS --; § 8 . EISENSTEIN SERIES AND THE CONTINUOUS SPECTRUM --; §9. THE TRACE FORMULA FOR GL(2) --; §10. AUTOMORPHIC FORMS ON A QUATERNION ALGEBRA --; BIBLIOGRAPHY --; INDEX
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400881611; 9783110494914; 9783110442496
• DOI: 10.1515/9781400881611
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Stephen S. Gelbart.

This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). 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.TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?