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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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Lectures on Modular Forms. (AM-48), Volume 48 / / Robert C. Gunning
| Lectures on Modular Forms. (AM-48), Volume 48 / / Robert C. Gunning |
| Autore | Gunning Robert C. |
| Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
| Descrizione fisica | 1 online resource (108 pages) : illustrations |
| Disciplina | 512.87 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Forms, Modular
Modular functions |
| Soggetto non controllato |
Automorphism
Big O notation Calculation Chain rule Change of variables Coefficient Compact Riemann surface Compact space Compactification (mathematics) Cusp form Differential form Dimension (vector space) Eisenstein series Ellipse Equivalence class Equivalence relation Euler characteristic Fourier series Fundamental domain Geometry Hilbert space Integer Linear combination Linear fractional transformation Linear map Linear subspace Local coordinates Meromorphic function Modular form Modular group Neighbourhood (mathematics) Quadratic form Quotient group Quotient space (topology) Requirement Riemann sphere Riemann surface Scientific notation Strong topology Subgroup Summation Theorem Uniformization theorem Upper half-plane Vector space |
| ISBN | 1-4008-8166-8 |
| Classificazione | SK 180 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- INTRODUCTION / Gunning, R . C . -- CONTENTS -- CHAPTER I. GEOMETRICAL BACKGROUND -- CHAPTER II. MODULAR FORMS -- CHAPTER III. POINCARÉ SERIES -- CHAPTER IV. EISENSTEIN SERIES -- CHAPTER V. MODULAR CORRESPONDENCES -- CHAPTER VI. QUADRATIC FORMS |
| Record Nr. | UNINA-9910154753603321 |
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Gunning Robert C.
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| Princeton, NJ : , : Princeton University Press, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Scattering Theory for Automorphic Functions. (AM-87), Volume 87 / / Peter D. Lax, Ralph S. Phillips
| Scattering Theory for Automorphic Functions. (AM-87), Volume 87 / / Peter D. Lax, Ralph S. Phillips |
| Autore | Lax Peter D. |
| Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
| Descrizione fisica | 1 online resource (313 pages) |
| Disciplina | 515.9 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Automorphic functions
Scattering (Mathematics) |
| Soggetto non controllato |
Absolute continuity
Algebra Analytic continuation Analytic function Annulus (mathematics) Asymptotic distribution Automorphic function Bilinear form Boundary (topology) Boundary value problem Bounded operator Calculation Cauchy sequence Change of variables Complex plane Conjugacy class Convolution Cusp neighborhood Cyclic group Derivative Differential equation Differential operator Dimension (vector space) Dimensional analysis Dirichlet integral Dirichlet series Eigenfunction Eigenvalues and eigenvectors Eisenstein series Elliptic operator Elliptic partial differential equation Equation Equivalence class Even and odd functions Existential quantification Explicit formula Explicit formulae (L-function) Exponential function Fourier transform Function space Functional analysis Functional calculus Fundamental domain Harmonic analysis Hilbert space Hyperbolic partial differential equation Infinitesimal generator (stochastic processes) Integral equation Integration by parts Invariant subspace Laplace operator Laplace transform Lebesgue measure Linear differential equation Linear space (geometry) Matrix (mathematics) Maximum principle Meromorphic function Modular group Neumann boundary condition Norm (mathematics) Null vector Number theory Operator theory Orthogonal complement Orthonormal basis Paley–Wiener theorem Partial differential equation Perturbation theory (quantum mechanics) Perturbation theory Primitive element (finite field) Principal component analysis Projection (linear algebra) Quadratic form Removable singularity Representation theorem Resolvent set Riemann hypothesis Riemann surface Riemann zeta function Riesz representation theorem Scatter matrix Scattering theory Schwarz reflection principle Selberg trace formula Self-adjoint Semigroup Sign (mathematics) Spectral theory Subgroup Subsequence Summation Support (mathematics) Theorem Trace class Trace formula Unitary operator Wave equation Weighted arithmetic mean Winding number |
| ISBN | 1-4008-8156-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- TABLE OF CONTENTS -- PREFACE -- LIST OF SYMBOLS -- §1. INTRODUCTION -- §2. AN ABSTRACT SCATTERING THEORY -- §3. A MODIFIED THEORY FOR SECOND ORDER EQUATIONS WITH AN INDEFINITE ENERGY FORM -- §4. THE LAPLACE-BELTRAMI OPERATOR FOR THE MODULAR GROUP -- §5. THE AUTOMORPHIC WAVE EQUATIONS -- §6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION -- §7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION -- §8. THE GENERAL CASE -- §9. THE SELBERG TRACE FORMULA -- REFERENCES -- INDEX -- Backmatter |
| Record Nr. | UNINA-9910154746703321 |
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Lax Peter D.
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| Princeton, NJ : , : Princeton University Press, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120 / / Laurent Clozel, James Arthur
| Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120 / / Laurent Clozel, James Arthur |
| Autore | Arthur James |
| Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
| Descrizione fisica | 1 online resource (248 pages) : illustrations |
| Disciplina | 512/.2 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Representations of groups
Trace formulas Automorphic forms |
| Soggetto non controllato |
0E
Addition Admissible representation Algebraic group Algebraic number field Approximation Archimedean property Automorphic form Automorphism Base change Big O notation Binomial coefficient Canonical map Cartan subalgebra Cartan subgroup Central simple algebra Characteristic polynomial Closure (mathematics) Combination Computation Conjecture Conjugacy class Connected component (graph theory) Continuous function Contradiction Corollary Counting Coxeter element Cusp form Cyclic permutation Dense set Density theorem Determinant Diagram (category theory) Discrete series representation Discrete spectrum Division algebra Eigenvalues and eigenvectors Eisenstein series Exact sequence Existential quantification Field extension Finite group Finite set Fourier transform Functor Fundamental lemma (Langlands program) Galois extension Galois group Global field Grothendieck group Group representation Haar measure Harmonic analysis Hecke algebra Hilbert's Theorem 90 Identity component Induced representation Infinite product Infinitesimal character Invariant measure Irreducibility (mathematics) Irreducible representation L-function Langlands classification Laurent series Lie algebra Lie group Linear algebraic group Local field Mathematical induction Maximal compact subgroup Multiplicative group Nilpotent group Orbital integral P-adic number Paley–Wiener theorem Parameter Parametrization Permutation Poisson summation formula Real number Reciprocal lattice Reductive group Root of unity Scientific notation Semidirect product Special case Spherical harmonics Subgroup Subset Summation Support (mathematics) Tensor product Theorem Trace formula Unitary representation Weil group Weyl group Zero of a function |
| ISBN | 1-4008-8240-0 |
| Classificazione | SK 240 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Introduction -- Chapter 1. Local Results -- Chapter 2. The Global Comparison -- Chapter 3. Base Change -- Bibliography |
| Record Nr. | UNINA-9910154743703321 |
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Arthur James
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| Princeton, NJ : , : Princeton University Press, , [2016] | ||
| 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 |
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Brubaker Ben <1976->
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| Princeton, N.J., : Princeton University Press, c2011 | ||
| 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 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 |
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Brubaker Ben <1976->
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| Princeton, N.J., : Princeton University Press, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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