Automorphic Representation of Unitary Groups in Three Variables. (AM-123), Volume 123 / / Jonathan David Rogawski |
Autore | Rogawski Jonathan David |
Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
Descrizione fisica | 1 online resource (273 pages) |
Disciplina | 512/.2 |
Collana | Annals of Mathematics Studies |
Soggetto topico |
Unitary groups
Trace formulas Representations of groups Automorphic forms |
Soggetto non controllato |
Abelian group
Abuse of notation Addition Admissible representation Algebraic closure Algebraic group Algebraic number field Asymptotic expansion Automorphism Base change map Base change Bijection Borel subgroup Cartan subgroup Class function (algebra) Coefficient Combination Compact group Complementary series representation Complex number Congruence subgroup Conjugacy class Continuous function Corollary Countable set Diagram (category theory) Differential operator Dimension (vector space) Dimension Discrete spectrum Division algebra Division by zero Eigenvalues and eigenvectors Embedding Equation Existential quantification Finite set Fourier transform Fundamental lemma (Langlands program) G factor (psychometrics) Galois group Global field Haar measure Hecke algebra Homomorphism Hyperbolic set Index notation Irreducible representation Isomorphism class L-function Langlands classification Linear combination Local field Mathematical induction Maximal compact subgroup Maximal torus Morphism Multiplicative group Neighbourhood (mathematics) Orbital integral Oscillator representation P-adic number Parity (mathematics) Principal series representation Quaternion algebra Quaternion Reductive group Regular element Remainder Representation theory Ring of integers Scientific notation Semisimple algebra Set (mathematics) Shimura variety Simple algebra Smoothness Special case Stable distribution Subgroup Summation Support (mathematics) Tate conjecture Tensor product Theorem Trace formula Triangular matrix Unitary group Variable (mathematics) Weight function Weil group |
ISBN | 1-4008-8244-3 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- Introduction -- Chapter 1. Preliminary definitions and notation -- Chapter 2. The trace formula -- Chapter 3. Stable conjugacy -- Chapter 4. Orbital integrals and endoscopic groups -- Chapter 5. Stabilization -- Chapter 6. Weighted orbital integrals -- Chapter 7. Elliptic singular terms -- Chapter 8. Germ expansions and limit formulas -- Chapter 9. Singularities -- Chapter 10. The stable trace formula -- Chapter 11. The Unitary group in two variables -- Chapter 12. Representation theory -- Chapter 13. Automorphic representations -- Chapter 14. Comparison of inner forms -- Chapter 15. Additional results -- References -- Subject Index -- Notation Index |
Record Nr. | UNINA-9910154747203321 |
Rogawski Jonathan David
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Princeton, NJ : , : Princeton University Press, , [2016] | ||
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Lo trovi qui: Univ. Federico II | ||
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Automorphic representations of low rank groups [[electronic resource] /] / Yuval Z. Flicker |
Autore | Flicker Yuval Z (Yuval Zvi), <1955-> |
Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2006 |
Descrizione fisica | 1 online resource (xi, 485 p.) |
Disciplina | 512.22 |
Soggetto topico |
Representations of groups
Unitary groups Lifting theory Automorphic forms Trace formulas |
Soggetto genere / forma | Electronic books. |
ISBN |
1-281-92488-1
9786611924881 981-277-362-2 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Preface -- pt. 1. On the symmetric square lifting introduction. 1. Functoriality and norms. 1.1. Hecke algebra. 1.2. Norms. 1.3. Local lifting. 1.4. Orthogonality. II. Orbital integrals. II.1. Fundamental lemma. II.2. Differential forms. II.3. Matching orbital integrals. II.4. Germ expansion. III. Twisted trace formula. III.1. Geometric side. III.2. Analytic side. III.3. Trace formulae. IV. Total global comparison. IV. Total global comparison. IV.1. The comparison. IV.2. Appendix: Mathematica program. V. Applications of a trace formula. V.1. Approximation. V.2. Main theorems. V.3. Characters and genericity. VI. Computation of a twisted character. VI.1. Proof of theorem, anisotropic case. VI.2. Proof of theorem, isotropic case -- pt. 2. Automorphic representations of the unitary group U(3,E/F) introduction. 1. Functorial overview. 2. Statement of results. I. Local theory. I.1. Conjugacy classes. I.2. Orbital integrals. I.3. Fundamental lemma. I.4. Admissible representations. I.5. Representations of U(2,1;C/R). 1.6. Fundamental lemma again. II. Trace formula. II.1. Stable trace formula. II.2. Twisted trace formula. II.3. Restricted comparison. II.4. Trace identity. II.5. The [symbol]-endo-lifting e'. II.6. The quasi-endo-lifting e. II.7. Unitary symmetric square. III. Liftings and packets. III.1. Local identity. III.2. Separation. III.3. Specific lifts. III.4. Whittaker models and twisted characters. III.5. Global lifting. III.6. Concluding remarks -- pt. 3. Zeta functions of Shimura varieties of U(3) introduction. 1. Statement of results. 2. The zeta function. I. Preliminaries. I.1. The Shumira variety. I.2. Decomposition of cohomology. I.3. Galois representations. II. Automorphic representations. II.1. Stabilization and the test function. II.2. Functorial overview of basechange for U(3). II.3. Local results on basechange for U(3). II.4. Global results on basechange for U(3). II.5. Spectral side of the stable trace formula. II.6. Proper endoscopic group. III. Local terms. III.1. The reflex field. III.2. The representation of the dual group. III.3. Local terms at p. III.4. The eigenvalues at p. III.5. Terms at p for the endoscopic group. IV. Real representations. IV.1. Representations of the real GL(2). IV.2. Representations of U(2,l). IV.3. Finite-dimensional representations. V. Galois representations. V.1. Stable case. V.2. Unstable case. V.3. Nontempered case. |
Record Nr. | UNINA-9910451547603321 |
Flicker Yuval Z (Yuval Zvi), <1955->
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Hackensack, N.J., : World Scientific, c2006 | ||
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Lo trovi qui: Univ. Federico II | ||
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Automorphic representations of low rank groups [[electronic resource] /] / Yuval Z. Flicker |
Autore | Flicker Yuval Z (Yuval Zvi), <1955-> |
Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2006 |
Descrizione fisica | 1 online resource (xi, 485 p.) |
Disciplina | 512.22 |
Soggetto topico |
Representations of groups
Unitary groups Lifting theory Automorphic forms Trace formulas |
ISBN |
1-281-92488-1
9786611924881 981-277-362-2 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Preface -- pt. 1. On the symmetric square lifting introduction. 1. Functoriality and norms. 1.1. Hecke algebra. 1.2. Norms. 1.3. Local lifting. 1.4. Orthogonality. II. Orbital integrals. II.1. Fundamental lemma. II.2. Differential forms. II.3. Matching orbital integrals. II.4. Germ expansion. III. Twisted trace formula. III.1. Geometric side. III.2. Analytic side. III.3. Trace formulae. IV. Total global comparison. IV. Total global comparison. IV.1. The comparison. IV.2. Appendix: Mathematica program. V. Applications of a trace formula. V.1. Approximation. V.2. Main theorems. V.3. Characters and genericity. VI. Computation of a twisted character. VI.1. Proof of theorem, anisotropic case. VI.2. Proof of theorem, isotropic case -- pt. 2. Automorphic representations of the unitary group U(3,E/F) introduction. 1. Functorial overview. 2. Statement of results. I. Local theory. I.1. Conjugacy classes. I.2. Orbital integrals. I.3. Fundamental lemma. I.4. Admissible representations. I.5. Representations of U(2,1;C/R). 1.6. Fundamental lemma again. II. Trace formula. II.1. Stable trace formula. II.2. Twisted trace formula. II.3. Restricted comparison. II.4. Trace identity. II.5. The [symbol]-endo-lifting e'. II.6. The quasi-endo-lifting e. II.7. Unitary symmetric square. III. Liftings and packets. III.1. Local identity. III.2. Separation. III.3. Specific lifts. III.4. Whittaker models and twisted characters. III.5. Global lifting. III.6. Concluding remarks -- pt. 3. Zeta functions of Shimura varieties of U(3) introduction. 1. Statement of results. 2. The zeta function. I. Preliminaries. I.1. The Shumira variety. I.2. Decomposition of cohomology. I.3. Galois representations. II. Automorphic representations. II.1. Stabilization and the test function. II.2. Functorial overview of basechange for U(3). II.3. Local results on basechange for U(3). II.4. Global results on basechange for U(3). II.5. Spectral side of the stable trace formula. II.6. Proper endoscopic group. III. Local terms. III.1. The reflex field. III.2. The representation of the dual group. III.3. Local terms at p. III.4. The eigenvalues at p. III.5. Terms at p for the endoscopic group. IV. Real representations. IV.1. Representations of the real GL(2). IV.2. Representations of U(2,l). IV.3. Finite-dimensional representations. V. Galois representations. V.1. Stable case. V.2. Unstable case. V.3. Nontempered case. |
Record Nr. | UNINA-9910777496103321 |
Flicker Yuval Z (Yuval Zvi), <1955->
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Hackensack, N.J., : World Scientific, c2006 | ||
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Lo trovi qui: Univ. Federico II | ||
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La formule des traces locale tordue / / Colette Moeglin, J.-L. Waldspurger |
Autore | Moeglin Colette <1953-> |
Pubbl/distr/stampa | Providence, RI : , : American Mathematical Society, , [2017] |
Descrizione fisica | 1 online resource (196 pages) |
Disciplina | 512.7/4 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Trace formulas
Twist mappings (Mathematics) Mappings (Mathematics) Algebraic number theory |
Soggetto genere / forma | Electronic books. |
ISBN | 1-4704-4280-9 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | fre |
Nota di contenuto | La formule des traces locale tordue -- La formule des traces locale torduesous forme symetrique. |
Record Nr. | UNINA-9910480206203321 |
Moeglin Colette <1953->
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Providence, RI : , : American Mathematical Society, , [2017] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
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La formule des traces locale tordue / / Colette Moeglin, J.-L. Waldspurger |
Autore | Moeglin Colette <1953-> |
Pubbl/distr/stampa | Providence, RI : , : American Mathematical Society, , [2017] |
Descrizione fisica | 1 online resource (196 pages) |
Disciplina | 512.7/4 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Trace formulas
Twist mappings (Mathematics) Mappings (Mathematics) Algebraic number theory |
ISBN | 1-4704-4280-9 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | fre |
Nota di contenuto | La formule des traces locale tordue -- La formule des traces locale torduesous forme symetrique. |
Record Nr. | UNINA-9910794927303321 |
Moeglin Colette <1953->
![]() |
||
Providence, RI : , : American Mathematical Society, , [2017] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
La formule des traces locale tordue / / Colette Moeglin, J.-L. Waldspurger |
Autore | Moeglin Colette <1953-> |
Pubbl/distr/stampa | Providence, RI : , : American Mathematical Society, , [2017] |
Descrizione fisica | 1 online resource (196 pages) |
Disciplina | 512.7/4 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Trace formulas
Twist mappings (Mathematics) Mappings (Mathematics) Algebraic number theory |
ISBN | 1-4704-4280-9 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | fre |
Nota di contenuto | La formule des traces locale tordue -- La formule des traces locale torduesous forme symetrique. |
Record Nr. | UNINA-9910827603303321 |
Moeglin Colette <1953->
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Providence, RI : , : American Mathematical Society, , [2017] | ||
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Lo trovi qui: Univ. Federico II | ||
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The fundamental lemma of the Shalika subgroup of GL(4) / / Solomon Friedberg, Hervé Jacquet |
Autore | Friedberg Solomon <1958-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1996 |
Descrizione fisica | 1 online resource (167 p.) |
Disciplina | 512/.7 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Automorphic forms
Trace formulas Representations of groups |
Soggetto genere / forma | Electronic books. |
ISBN | 1-4704-0179-7 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""Chapter I. Introduction and Statement of Results""; ""1. Introduction""; ""2. The Shalika Subgroup H of GL(4): Relevant Double Cosets and Kloosterman Integrals""; ""3. The Symplectic Group GS[sub(p)](4): Relevant Double Cosets and Kloosterman Integrals""; ""4. The Main Theorem""; ""5. Kloosterman Integrals and Gauss Sums""; ""Chapter II. Evaluation of the Integral for the Main H-Relevant Double Cosets""; ""1. Plan of the Computation""; ""2. The Unipotent Integral""; ""3. The Toroidal Integral""; ""4. Two Supplementary Integrals""
""5. Evaluation of the Mellin Transform I: The Ramified Case""""6. Evaluation of the Mellin Transform II: The Case Ï?[sub(1)]Ramified, Ï?[sub(2)] Unramified""; ""7. Evaluation of the Mellin Transform III: The Case Ï?[sub(1)]Unramified, Ï?[sub(2)]Ramified""; ""8. Evaluation of the Mellin Transform IV: The Unramified Case""; ""Chapter III. Evaluation of the Integrals for the Other if-Relevant Double Cosets""; ""1. Evaluation of the Integral M[sub(F)](Ï?[sub(1); 1), I: Unipotent Integration""; ""2. Evaluation of the Integral M[sub(F)](Ï?[sub(1); 1), II: Toroidal Integration and Simplification"" ""3. Evaluation of the Integral M[sub(F)](Ï?[sub(1)132), I: Unipotent Integration""; ""4. Evaluation of the Integral M[sub(F)](Ï?[sub(1); 132), II: Toroidal Integration and Simplification""; ""Chapter IV. Evaluation of the GS[sub(p)](4) Integral for the Main Double Cosets""; ""1. Computation of the Integral J(t)""; ""2. Simplification of the Integrals Giving J(t)""; ""3. Computation of the Mellin Transform""; ""4. Evaluation of the Mellin Transform I: The Ramified Case""; ""5. Evaluation of the Mellin Transform II: The Case Ï?[sub(1)] Ramified, Ï?[sub(2)] Unramified"" ""6. Evaluation of the Mellin Transform III: The Case Ï?[sub(1)] Unramified, Ï?[sub(2)] Ramified""""7. Evaluation of the Mellin Transform IV: The Unramified Case""; ""Chapter V. Evaluation of the G5[sub(p)](4) Integrals for the Other Relevant Double Cosets""; ""1. Computation of the Integral J(Ï?[sub(1)],t)""; ""2. Evaluation of the Mellin Transform M[sub(J)](Ï?Ï?[sub(1)])""; ""3. Computation of the Integral J(Ï?[sub(2)],t)""; ""4. Evaluation of the Mellin Transform M[sub(J)](Ï?Ï?[sub(1)])""; ""References"" |
Record Nr. | UNINA-9910480027603321 |
Friedberg Solomon <1958->
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Providence, Rhode Island : , : American Mathematical Society, , 1996 | ||
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Lo trovi qui: Univ. Federico II | ||
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The fundamental lemma of the Shalika subgroup of GL(4) / / Solomon Friedberg, Hervé Jacquet |
Autore | Friedberg Solomon <1958-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1996 |
Descrizione fisica | 1 online resource (167 p.) |
Disciplina | 512/.7 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Automorphic forms
Trace formulas Representations of groups |
ISBN | 1-4704-0179-7 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""Chapter I. Introduction and Statement of Results""; ""1. Introduction""; ""2. The Shalika Subgroup H of GL(4): Relevant Double Cosets and Kloosterman Integrals""; ""3. The Symplectic Group GS[sub(p)](4): Relevant Double Cosets and Kloosterman Integrals""; ""4. The Main Theorem""; ""5. Kloosterman Integrals and Gauss Sums""; ""Chapter II. Evaluation of the Integral for the Main H-Relevant Double Cosets""; ""1. Plan of the Computation""; ""2. The Unipotent Integral""; ""3. The Toroidal Integral""; ""4. Two Supplementary Integrals""
""5. Evaluation of the Mellin Transform I: The Ramified Case""""6. Evaluation of the Mellin Transform II: The Case Ï?[sub(1)]Ramified, Ï?[sub(2)] Unramified""; ""7. Evaluation of the Mellin Transform III: The Case Ï?[sub(1)]Unramified, Ï?[sub(2)]Ramified""; ""8. Evaluation of the Mellin Transform IV: The Unramified Case""; ""Chapter III. Evaluation of the Integrals for the Other if-Relevant Double Cosets""; ""1. Evaluation of the Integral M[sub(F)](Ï?[sub(1); 1), I: Unipotent Integration""; ""2. Evaluation of the Integral M[sub(F)](Ï?[sub(1); 1), II: Toroidal Integration and Simplification"" ""3. Evaluation of the Integral M[sub(F)](Ï?[sub(1)132), I: Unipotent Integration""; ""4. Evaluation of the Integral M[sub(F)](Ï?[sub(1); 132), II: Toroidal Integration and Simplification""; ""Chapter IV. Evaluation of the GS[sub(p)](4) Integral for the Main Double Cosets""; ""1. Computation of the Integral J(t)""; ""2. Simplification of the Integrals Giving J(t)""; ""3. Computation of the Mellin Transform""; ""4. Evaluation of the Mellin Transform I: The Ramified Case""; ""5. Evaluation of the Mellin Transform II: The Case Ï?[sub(1)] Ramified, Ï?[sub(2)] Unramified"" ""6. Evaluation of the Mellin Transform III: The Case Ï?[sub(1)] Unramified, Ï?[sub(2)] Ramified""""7. Evaluation of the Mellin Transform IV: The Unramified Case""; ""Chapter V. Evaluation of the G5[sub(p)](4) Integrals for the Other Relevant Double Cosets""; ""1. Computation of the Integral J(Ï?[sub(1)],t)""; ""2. Evaluation of the Mellin Transform M[sub(J)](Ï?Ï?[sub(1)])""; ""3. Computation of the Integral J(Ï?[sub(2)],t)""; ""4. Evaluation of the Mellin Transform M[sub(J)](Ï?Ï?[sub(1)])""; ""References"" |
Record Nr. | UNINA-9910788730703321 |
Friedberg Solomon <1958->
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Providence, Rhode Island : , : American Mathematical Society, , 1996 | ||
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Lo trovi qui: Univ. Federico II | ||
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The fundamental lemma of the Shalika subgroup of GL(4) / / Solomon Friedberg, Hervé Jacquet |
Autore | Friedberg Solomon <1958-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1996 |
Descrizione fisica | 1 online resource (167 p.) |
Disciplina | 512/.7 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Automorphic forms
Trace formulas Representations of groups |
ISBN | 1-4704-0179-7 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""Chapter I. Introduction and Statement of Results""; ""1. Introduction""; ""2. The Shalika Subgroup H of GL(4): Relevant Double Cosets and Kloosterman Integrals""; ""3. The Symplectic Group GS[sub(p)](4): Relevant Double Cosets and Kloosterman Integrals""; ""4. The Main Theorem""; ""5. Kloosterman Integrals and Gauss Sums""; ""Chapter II. Evaluation of the Integral for the Main H-Relevant Double Cosets""; ""1. Plan of the Computation""; ""2. The Unipotent Integral""; ""3. The Toroidal Integral""; ""4. Two Supplementary Integrals""
""5. Evaluation of the Mellin Transform I: The Ramified Case""""6. Evaluation of the Mellin Transform II: The Case Ï?[sub(1)]Ramified, Ï?[sub(2)] Unramified""; ""7. Evaluation of the Mellin Transform III: The Case Ï?[sub(1)]Unramified, Ï?[sub(2)]Ramified""; ""8. Evaluation of the Mellin Transform IV: The Unramified Case""; ""Chapter III. Evaluation of the Integrals for the Other if-Relevant Double Cosets""; ""1. Evaluation of the Integral M[sub(F)](Ï?[sub(1); 1), I: Unipotent Integration""; ""2. Evaluation of the Integral M[sub(F)](Ï?[sub(1); 1), II: Toroidal Integration and Simplification"" ""3. Evaluation of the Integral M[sub(F)](Ï?[sub(1)132), I: Unipotent Integration""; ""4. Evaluation of the Integral M[sub(F)](Ï?[sub(1); 132), II: Toroidal Integration and Simplification""; ""Chapter IV. Evaluation of the GS[sub(p)](4) Integral for the Main Double Cosets""; ""1. Computation of the Integral J(t)""; ""2. Simplification of the Integrals Giving J(t)""; ""3. Computation of the Mellin Transform""; ""4. Evaluation of the Mellin Transform I: The Ramified Case""; ""5. Evaluation of the Mellin Transform II: The Case Ï?[sub(1)] Ramified, Ï?[sub(2)] Unramified"" ""6. Evaluation of the Mellin Transform III: The Case Ï?[sub(1)] Unramified, Ï?[sub(2)] Ramified""""7. Evaluation of the Mellin Transform IV: The Unramified Case""; ""Chapter V. Evaluation of the G5[sub(p)](4) Integrals for the Other Relevant Double Cosets""; ""1. Computation of the Integral J(Ï?[sub(1)],t)""; ""2. Evaluation of the Mellin Transform M[sub(J)](Ï?Ï?[sub(1)])""; ""3. Computation of the Integral J(Ï?[sub(2)],t)""; ""4. Evaluation of the Mellin Transform M[sub(J)](Ï?Ï?[sub(1)])""; ""References"" |
Record Nr. | UNINA-9910812407003321 |
Friedberg Solomon <1958->
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Providence, Rhode Island : , : American Mathematical Society, , 1996 | ||
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Lo trovi qui: Univ. Federico II | ||
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Kuznetsov's trace formula and the Hecke eigenvalues of Maass forms / / A. Knightly, C. Li |
Autore | Knightly Andrew <1972-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2012 |
Descrizione fisica | 1 online resource (132 p.) |
Disciplina | 512.7 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Hecke operators
Trace formulas |
Soggetto genere / forma | Electronic books. |
ISBN | 1-4704-1006-0 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | ""9.1. A bound for twisted Kloosterman sums""""9.2. Factorization""; ""9.3. Proof of Theorem 9.2""; ""Chapter 10. Equidistribution of Hecke eigenvalues""; ""Bibliography""; ""Notation index""; ""Subject index"" |
Record Nr. | UNINA-9910480538503321 |
Knightly Andrew <1972->
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Providence, Rhode Island : , : American Mathematical Society, , 2012 | ||
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Lo trovi qui: Univ. Federico II | ||
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