Automorphic Forms on Adele Groups. (AM-83), Volume 83 / / Stephen S. Gelbart
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| Autore: |
Gelbart Stephen S.
|
| Titolo: |
Automorphic Forms on Adele Groups. (AM-83), Volume 83 / / Stephen S. Gelbart
|
| Pubblicazione: | Princeton, NJ : , : Princeton University Press, , [2016] |
| ©1975 | |
| Descrizione fisica: | 1 online resource (280 pages) |
| Disciplina: | 512/.22 |
| Soggetto topico: | Representations of groups |
| Automorphic forms | |
| Linear algebraic groups | |
| Adeles | |
| Soggetto non controllato: | Abelian extension |
| Abelian group | |
| Absolute value | |
| Addition | |
| Additive group | |
| Algebraic group | |
| Algebraic number field | |
| Algebraic number theory | |
| Analytic continuation | |
| Analytic function | |
| Arbitrarily large | |
| Automorphic form | |
| Cartan subgroup | |
| Class field theory | |
| Complex space | |
| Congruence subgroup | |
| Conjugacy class | |
| Coprime integers | |
| Cusp form | |
| Differential equation | |
| Dimension (vector space) | |
| Direct integral | |
| Direct sum | |
| Division algebra | |
| Eigenfunction | |
| Eigenvalues and eigenvectors | |
| Eisenstein series | |
| Euler product | |
| Existential quantification | |
| Exponential function | |
| Factorization | |
| Finite field | |
| Formal power series | |
| Fourier series | |
| Fourier transform | |
| Fuchsian group | |
| Function (mathematics) | |
| Function space | |
| Functional equation | |
| Fundamental unit (number theory) | |
| Galois extension | |
| Global field | |
| Group algebra | |
| Group representation | |
| Haar measure | |
| Harish-Chandra | |
| Hecke L-function | |
| Hilbert space | |
| Homomorphism | |
| Induced representation | |
| Infinite product | |
| Inner automorphism | |
| Integer | |
| Invariant measure | |
| Invariant subspace | |
| Irreducible representation | |
| L-function | |
| Lie algebra | |
| Linear map | |
| Matrix coefficient | |
| Mellin transform | |
| Meromorphic function | |
| Modular form | |
| P-adic number | |
| Poisson summation formula | |
| Prime ideal | |
| Prime number | |
| Principal series representation | |
| Projective representation | |
| Quadratic field | |
| Quadratic form | |
| Quaternion algebra | |
| Quaternion | |
| Real number | |
| Regular representation | |
| Representation theory | |
| Ring (mathematics) | |
| Ring of integers | |
| Scientific notation | |
| Selberg trace formula | |
| Simple algebra | |
| Square-integrable function | |
| Sub"ient | |
| Subgroup | |
| Summation | |
| Theorem | |
| Theory | |
| Theta function | |
| Topological group | |
| Topology | |
| Trace formula | |
| Trivial representation | |
| Uniqueness theorem | |
| Unitary operator | |
| Unitary representation | |
| Universal enveloping algebra | |
| Upper half-plane | |
| Variable (mathematics) | |
| Vector space | |
| Weil group | |
| Note generali: | Bibliographic Level Mode of Issuance: Monograph |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | 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 |
| Sommario/riassunto: | 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? |
| Titolo autorizzato: | Automorphic Forms on Adele Groups. (AM-83), Volume 83 |
| ISBN: | 1-4008-8161-7 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910154753203321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Annals of mathematics studies ; ; Number 83.