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Automorphic Forms on Adele Groups. (AM-83), Volume 83 / / Stephen S. Gelbart
| Automorphic Forms on Adele Groups. (AM-83), Volume 83 / / Stephen S. Gelbart |
| Autore | Gelbart Stephen S. |
| Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
| Descrizione fisica | 1 online resource (280 pages) |
| Disciplina | 512/.22 |
| Collana | Annals of Mathematics Studies |
| 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 |
| ISBN | 1-4008-8161-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910154753203321 |
Gelbart Stephen S.
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| Princeton, NJ : , : Princeton University Press, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The Gross-Zagier formula on Shimura curves [[electronic resource] /] / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang
| The Gross-Zagier formula on Shimura curves [[electronic resource] /] / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang |
| Autore | Yuan Xinyi <1981-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, : Princeton University Press, 2012, c2013 |
| Descrizione fisica | 1 online resource (267 p.) |
| Disciplina | 516.3/52 |
| Altri autori (Persone) |
ZhangShouwu
ZhangWei <1981-> |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Shimura varieties
Arithmetical algebraic geometry Automorphic forms Quaternions |
| Soggetto non controllato |
Arakelov theory
Benedict Gross Don Zagier EichlerГhimura theory Eisenstein series GrossКagier formula Heegner point Hodge bundle Hodge index theorem L-series MordellЗeil group NeronДate height RankinГelberg L-function Schwartz function Shimizu lifting Shimura curve Shimura curves SiegelЗeil formula Waldspurger formula Weil representation abelian varieties analytic kernel function analytic kernel degenerate Schwartz function discrete series generating series geometric kernel height series holomorphic kernel function holomorphic projection incoherent Eisenstein series incoherent automorphic representation incoherent quaternion algebra kernel function kernel identity local height modular curve modularity multiplicity function non-archimedean local field non-degenerate quadratic space ordinary component orthogonal space projector pull-back formula ramified quadratic extension supersingular component superspecial component theta function theta liftings theta series trace identity un-normalized kernel function unramified quadratic extension |
| ISBN |
9786613883919
1-4008-4564-5 1-283-57146-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Preface -- Chapter One. Introduction and Statement of Main Results -- Chapter Two. Weil Representation and Waldspurger Formula -- Chapter Three. Mordell-Weil Groups and Generating Series -- Chapter Four. Trace of the Generating Series -- Chapter Five. Assumptions on the Schwartz Function -- Chapter Six. Derivative of the Analytic Kernel -- Chapter Seven. Decomposition of the Geometric Kernel -- Chapter Eight. Local Heights of CM Points -- Bibliography -- Index |
| Record Nr. | UNINA-9910790961403321 |
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Yuan Xinyi <1981->
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| Princeton, : Princeton University Press, 2012, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Weyl group multiple Dirichlet [[electronic resource] /] / Ben Brubaker, Daniel Bump, and Solomon Friedberg
| Weyl group multiple Dirichlet [[electronic resource] /] / Ben Brubaker, Daniel Bump, and Solomon Friedberg |
| Autore | Brubaker Ben <1976-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, c2011 |
| Descrizione fisica | 1 online resource (173 p.) |
| Disciplina | 515/.243 |
| Altri autori (Persone) |
BumpDaniel <1952->
FriedbergSolomon <1958-> |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Dirichlet series
Weyl groups |
| Soggetto genere / forma | Electronic books. |
| Soggetto non controllato |
BZL pattern
Class I. Eisenstein series Euler product Gauss sum Gelfand-Tsetlin pattern Kashiwara operator Kashiwara's crystal Knowability Lemma Kostant partition function Riemann zeta function Schur polynomial Schützenberger involution Snake Lemma Statement A. Statement B. Statement C. Statement D. Statement E. Statement F. Statement G. Tokuyama's Theorem Weyl character formula Weyl denominator Weyl group multiple Dirichlet series Weyl vector Whittaker coefficient Whittaker function Yang-Baxter equation Yang–Baxter equation accordion adele group affine linear transformation analytic continuation analytic number theory archimedean place basis vector bijection bookkeeping box-circle duality boxing canonical indexings cardinality cartoon circling class combinatorial identity concurrence critical resonance crystal base crystal graph crystal divisibility condition double sum episode equivalence relation f-packet free abelian group functional equation generating function global field ice-type model inclusion-exclusion indexing involution isomorphism knowability maximality nodal signature nonarchimedean local field noncritical resonance nonzero contribution p-adic group p-adic integral p-adic integration partition function polynomial preaccordion prototype reduced root system representation theory residue class field resonance resotope row sums row transfer matrix short pattern six-vertex model snakes statistical mechanics subsignature tableaux type Γ-equivalence class Γ-swap |
| ISBN |
1-283-01338-X
9786613013385 1-4008-3899-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Chapter One. Type A Weyl Group Multiple Dirichlet Series -- Chapter Two. Crystals and Gelfand-Tsetlin Patterns -- Chapter Three. Duality -- Chapter Four. Whittaker Functions -- Chapter Five. Tokuyama's Theorem -- Chapter Six. Outline of the Proof -- Chapter Seven. Statement B Implies Statement A -- Chapter Eight. Cartoons -- Chapter Nine. Snakes -- Chapter Ten. Noncritical Resonances -- Chapter Eleven. Types -- Chapter Twelve. Knowability -- Chapter Thirteen. The Reduction to Statement D -- Chapter Fourteen. Statement E Implies Statement D -- Chapter Fifteen. Evaluation of ΛΓ and ΛΔ, and Statement G -- Chapter Sixteen. Concurrence -- Chapter Seventeen. Conclusion of the Proof -- Chapter Eighteen. Statement B and Crystal Graphs -- Chapter Nineteen. Statement B and the Yang-Baxter Equation -- Chapter Twenty. Crystals and p-adic Integration -- Bibliography -- Notation -- Index |
| Record Nr. | UNINA-9910459795903321 |
|
Brubaker Ben <1976->
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| Princeton, N.J., : Princeton University Press, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Weyl group multiple Dirichlet [[electronic resource] /] / Ben Brubaker, Daniel Bump, and Solomon Friedberg
| Weyl group multiple Dirichlet [[electronic resource] /] / Ben Brubaker, Daniel Bump, and Solomon Friedberg |
| Autore | Brubaker Ben <1976-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, c2011 |
| Descrizione fisica | 1 online resource (173 p.) |
| Disciplina | 515/.243 |
| Altri autori (Persone) |
BumpDaniel <1952->
FriedbergSolomon <1958-> |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Dirichlet series
Weyl groups |
| Soggetto non controllato |
BZL pattern
Class I. Eisenstein series Euler product Gauss sum Gelfand-Tsetlin pattern Kashiwara operator Kashiwara's crystal Knowability Lemma Kostant partition function Riemann zeta function Schur polynomial Schützenberger involution Snake Lemma Statement A. Statement B. Statement C. Statement D. Statement E. Statement F. Statement G. Tokuyama's Theorem Weyl character formula Weyl denominator Weyl group multiple Dirichlet series Weyl vector Whittaker coefficient Whittaker function Yang-Baxter equation Yang–Baxter equation accordion adele group affine linear transformation analytic continuation analytic number theory archimedean place basis vector bijection bookkeeping box-circle duality boxing canonical indexings cardinality cartoon circling class combinatorial identity concurrence critical resonance crystal base crystal graph crystal divisibility condition double sum episode equivalence relation f-packet free abelian group functional equation generating function global field ice-type model inclusion-exclusion indexing involution isomorphism knowability maximality nodal signature nonarchimedean local field noncritical resonance nonzero contribution p-adic group p-adic integral p-adic integration partition function polynomial preaccordion prototype reduced root system representation theory residue class field resonance resotope row sums row transfer matrix short pattern six-vertex model snakes statistical mechanics subsignature tableaux type Γ-equivalence class Γ-swap |
| ISBN |
1-283-01338-X
9786613013385 1-4008-3899-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Chapter One. Type A Weyl Group Multiple Dirichlet Series -- Chapter Two. Crystals and Gelfand-Tsetlin Patterns -- Chapter Three. Duality -- Chapter Four. Whittaker Functions -- Chapter Five. Tokuyama's Theorem -- Chapter Six. Outline of the Proof -- Chapter Seven. Statement B Implies Statement A -- Chapter Eight. Cartoons -- Chapter Nine. Snakes -- Chapter Ten. Noncritical Resonances -- Chapter Eleven. Types -- Chapter Twelve. Knowability -- Chapter Thirteen. The Reduction to Statement D -- Chapter Fourteen. Statement E Implies Statement D -- Chapter Fifteen. Evaluation of ΛΓ and ΛΔ, and Statement G -- Chapter Sixteen. Concurrence -- Chapter Seventeen. Conclusion of the Proof -- Chapter Eighteen. Statement B and Crystal Graphs -- Chapter Nineteen. Statement B and the Yang-Baxter Equation -- Chapter Twenty. Crystals and p-adic Integration -- Bibliography -- Notation -- Index |
| Record Nr. | UNINA-9910789812403321 |
|
Brubaker Ben <1976->
|
||
| Princeton, N.J., : Princeton University Press, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||