Automorphic Forms on Adele Groups. (AM-83), Volume 83 / / 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 dev...
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| Superior document: | Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1975 |
| 出版年: | 2016 |
| 言語: | English |
| シリーズ: | Annals of Mathematics Studies ;
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| 物理的記述: | 1 online resource (227 p.) |
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Gelbart, Stephen S., author. aut http://id.loc.gov/vocabulary/relators/aut Automorphic Forms on Adele Groups. (AM-83), Volume 83 / Stephen S. Gelbart. Princeton, NJ : Princeton University Press, [2016] ©1975 1 online resource (227 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 83 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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? Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Adeles. Automorphic forms. Linear algebraic groups. Representations of groups. MATHEMATICS / Group Theory. bisacsh 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. Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691081564 https://doi.org/10.1515/9781400881611 https://www.degruyter.com/isbn/9781400881611 Cover https://www.degruyter.com/document/cover/isbn/9781400881611/original |
| language |
English |
| format |
eBook |
| author |
Gelbart, Stephen S., Gelbart, Stephen S., |
| spellingShingle |
Gelbart, Stephen S., Gelbart, Stephen S., Automorphic Forms on Adele Groups. (AM-83), Volume 83 / Annals of Mathematics Studies ; 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 |
| author_facet |
Gelbart, Stephen S., Gelbart, Stephen S., |
| author_variant |
s s g ss ssg s s g ss ssg |
| author_role |
VerfasserIn VerfasserIn |
| author_sort |
Gelbart, Stephen S., |
| title |
Automorphic Forms on Adele Groups. (AM-83), Volume 83 / |
| title_full |
Automorphic Forms on Adele Groups. (AM-83), Volume 83 / Stephen S. Gelbart. |
| title_fullStr |
Automorphic Forms on Adele Groups. (AM-83), Volume 83 / Stephen S. Gelbart. |
| title_full_unstemmed |
Automorphic Forms on Adele Groups. (AM-83), Volume 83 / Stephen S. Gelbart. |
| title_auth |
Automorphic Forms on Adele Groups. (AM-83), Volume 83 / |
| title_alt |
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 |
| title_new |
Automorphic Forms on Adele Groups. (AM-83), Volume 83 / |
| title_sort |
automorphic forms on adele groups. (am-83), volume 83 / |
| series |
Annals of Mathematics Studies ; |
| series2 |
Annals of Mathematics Studies ; |
| publisher |
Princeton University Press, |
| publishDate |
2016 |
| physical |
1 online resource (227 p.) Issued also in print. |
| contents |
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 |
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9781400881611 9783110494914 9783110442496 9780691081564 |
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Q - Science |
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QA - Mathematics |
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QA171 |
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QA 3171 G39 41975EB |
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https://doi.org/10.1515/9781400881611 https://www.degruyter.com/isbn/9781400881611 https://www.degruyter.com/document/cover/isbn/9781400881611/original |
| illustrated |
Not Illustrated |
| dewey-hundreds |
500 - Science |
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510 - Mathematics |
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512 - Algebra |
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512/.22 |
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3512 222 |
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512/.22 |
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512/.22 |
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10.1515/9781400881611 |
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Automorphic Forms on Adele Groups. (AM-83), Volume 83 / |
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