Automorphic forms on Adele groups
著者
書誌事項
Automorphic forms on Adele groups
（Annals of mathematics studies, no. 83）
Princeton University Press, c1975
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注記
Expanded from notes mimeographed at Cornell in May of 1972 and entitled Automorphic forms and representations of Adele groups
Bibliography: p. 260-263
Includes index
内容説明・目次
内容説明
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 Algebra
目次
*Frontmatter, pg. i*PREFACE, pg. vii*CONTENTS, pg. ix* 1. THE CLASSICAL THEORY, pg. 1* 2. AUTOMORPHIC FORMS AND THE DECOMPOSITION OF L2(GAMMA\SL(2, )), pg. 22* 3. AUTOMORPHIC FORMS AS FUNCTIONS ON THE ADELE GROUP OF GL(2), pg. 40* 4. THE REPRESENTATIONS OF GL(2) OVER LOCAL AND GLOBAL FIELDS, pg. 54* 5 . CUSP FORMS AND REPRESENTATIONS OF THE ADELE GROUP OF GL(2), pg. 79* 6. HECKE THEORY FOR GL(2), pg. 98* 7 . THE CONSTRUCTION OF A SPECIAL CLASS OF AUTOMORPHIC FORMS, pg. 133* 8 . EISENSTEIN SERIES AND THE CONTINUOUS SPECTRUM, pg. 161* 9. THE TRACE FORMULA FOR GL(2), pg. 181* 10. AUTOMORPHIC FORMS ON A QUATERNION ALGEBRA, pg. 227*BIBLIOGRAPHY, pg. 260*INDEX, pg. 264
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