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Geometry and analysis of automorphic forms of several variables [[electronic resource] ] : proceedings of the international symposium in honor of Takayuki Oda on the occasion of his 60th birthday, Tokyo, Japan, 14-17 September, 2009 / / editors, Yoshinori Hamahata ... [et al.]
| Geometry and analysis of automorphic forms of several variables [[electronic resource] ] : proceedings of the international symposium in honor of Takayuki Oda on the occasion of his 60th birthday, Tokyo, Japan, 14-17 September, 2009 / / editors, Yoshinori Hamahata ... [et al.] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (388 p.) |
| Disciplina | 515.94 |
| Altri autori (Persone) |
OdaTakayuki
HamahataYoshinori |
| Collana | Series on number theory and its application |
| Soggetto topico |
Geometry
Automorphic forms |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-37603-1
9786613555410 981-4355-60-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Program of symposium; Contents; The Birch and Swinnerton-Dyer conjecture for Q-curves and Oda's period relations Henri Darmon, Victor Rotger and Yu Zhao; 1. Introduction; 2. Background; 2.1. The Birch and Swinnerton-Dyer conjecture in low analytic rank; 2.2. Oda's period relations and ATR points; 3. The Birch and Swinnerton-Dyer conjecture for Q-curves; 3.1. Review of Q-curves; 3.2. The main result; 4. Heegner points on Shimura's elliptic curves; 4.1. An explicit Heegner point construction; 4.2. Heegner points and ATR cycles; 4.3. Numerical examples; 4.4. Proof of Proposition 4.1
ReferencesThe supremum of Newton polygons of p-divisible groups with a given p-kernel type Shushi Harashita; 1. Introduction; 2. A catalogue of p-divisible groups with a given type; 3. Preliminaries on F-zips; 4. Lifting of F-zips; 5. A reduction of the problem; 6. Extensions by a minimal p-divisible group; 7. Proof of Proposition 5.2; References; Borcherds lifts on Sp2(Z) Bernhard Heim and Atsushi Murase; 1. Introduction and the main results; 1.1. Introduction; 1.2. Siegel modular forms; 1.3. The organization of the paper; 1.4. Notation; 2. Borcherds lifts; 2.1. Jacobi forms 2.2. Humbert surfaces2.3. Siegel modular forms with a nontrivial character; 2.4. Borcherds lifts on; 2.5. Examples of Borcherds lifts; 3. Proof of the main results; 3.1. The multiplicative symmetry; 3.2. A characterization of powers of the modular discriminant; 3.3. The multiplicative symmetry for Sym2(Mk( 1)); 3.4. Proofs of Theorem 1.1 and Theorem 1.2 (i); 4. The weight formula; 4.1. Cohen numbers; 4.2. The weight formula for Borcherds lifts; Acknowledgement; References; The archimedean Whittaker functions on GL(3) Miki Hirano, Taku Ishii and Tadashi Miyazaki; 1. Introduction 2. Preliminaries2.1. Notation; 2.2. Basic objects; 2.3. Whittaker functions on Gn; 2.5. The contragradient Whittaker functions; 2.6. The generalized principal series representations of Gn = GL(n; R); 2.7. The principal series representations of Gn = GL(n; C); 3. Whittaker functions on G3 = GL(3; R); 3.1. Irreducible representations of K3 = O(3); 3.2. Whittaker functions on G3 = GL(3; R) at the minimal K3-types; 3.3. Whittaker functions on G3 = GL(3; R) at the multiplicity one K3-types; 4. Whittaker functions on G3 = GL(3; C); 4.1. Irreducible representations of K3 = U(3) 4.2. Whittaker functions on G3 = GL(3 C) at the minimal K3-types; 5. The archimedean local theory of the standard L-functions for GL(n1) GL(n2) (n1 > n2); 5.1. The local Langlands correspondence for GL(n) over R; 5.2. The local Langlands correspondence for GL(n) over C; 5.3. The archimedean zeta integrals for GL(n1) GL(n2) (n1 > n2); 6. Calculus of the archimedean zeta integrals; 6.1. The archimedean zeta integrals for GL(3) GL(1); 6.2. The proof of Theorem 6.1; 6.3. The archimedean zeta integrals for GL(3) GL(2); References Arithmetic properties of p-adic elliptic logarithmic functions Noriko Hirata-Kohno |
| Record Nr. | UNINA-9910457431203321 |
| Singapore ; ; Hackensack, N.J., : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometry and analysis of automorphic forms of several variables [[electronic resource] ] : proceedings of the international symposium in honor of Takayuki Oda on the occasion of his 60th birthday, Tokyo, Japan, 14-17 September, 2009 / / editors, Yoshinori Hamahata ... [et al.]
| Geometry and analysis of automorphic forms of several variables [[electronic resource] ] : proceedings of the international symposium in honor of Takayuki Oda on the occasion of his 60th birthday, Tokyo, Japan, 14-17 September, 2009 / / editors, Yoshinori Hamahata ... [et al.] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (388 p.) |
| Disciplina | 515.94 |
| Altri autori (Persone) |
OdaTakayuki
HamahataYoshinori |
| Collana | Series on number theory and its application |
| Soggetto topico |
Geometry
Automorphic forms |
| ISBN |
1-280-37603-1
9786613555410 981-4355-60-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Program of symposium; Contents; The Birch and Swinnerton-Dyer conjecture for Q-curves and Oda's period relations Henri Darmon, Victor Rotger and Yu Zhao; 1. Introduction; 2. Background; 2.1. The Birch and Swinnerton-Dyer conjecture in low analytic rank; 2.2. Oda's period relations and ATR points; 3. The Birch and Swinnerton-Dyer conjecture for Q-curves; 3.1. Review of Q-curves; 3.2. The main result; 4. Heegner points on Shimura's elliptic curves; 4.1. An explicit Heegner point construction; 4.2. Heegner points and ATR cycles; 4.3. Numerical examples; 4.4. Proof of Proposition 4.1
ReferencesThe supremum of Newton polygons of p-divisible groups with a given p-kernel type Shushi Harashita; 1. Introduction; 2. A catalogue of p-divisible groups with a given type; 3. Preliminaries on F-zips; 4. Lifting of F-zips; 5. A reduction of the problem; 6. Extensions by a minimal p-divisible group; 7. Proof of Proposition 5.2; References; Borcherds lifts on Sp2(Z) Bernhard Heim and Atsushi Murase; 1. Introduction and the main results; 1.1. Introduction; 1.2. Siegel modular forms; 1.3. The organization of the paper; 1.4. Notation; 2. Borcherds lifts; 2.1. Jacobi forms 2.2. Humbert surfaces2.3. Siegel modular forms with a nontrivial character; 2.4. Borcherds lifts on; 2.5. Examples of Borcherds lifts; 3. Proof of the main results; 3.1. The multiplicative symmetry; 3.2. A characterization of powers of the modular discriminant; 3.3. The multiplicative symmetry for Sym2(Mk( 1)); 3.4. Proofs of Theorem 1.1 and Theorem 1.2 (i); 4. The weight formula; 4.1. Cohen numbers; 4.2. The weight formula for Borcherds lifts; Acknowledgement; References; The archimedean Whittaker functions on GL(3) Miki Hirano, Taku Ishii and Tadashi Miyazaki; 1. Introduction 2. Preliminaries2.1. Notation; 2.2. Basic objects; 2.3. Whittaker functions on Gn; 2.5. The contragradient Whittaker functions; 2.6. The generalized principal series representations of Gn = GL(n; R); 2.7. The principal series representations of Gn = GL(n; C); 3. Whittaker functions on G3 = GL(3; R); 3.1. Irreducible representations of K3 = O(3); 3.2. Whittaker functions on G3 = GL(3; R) at the minimal K3-types; 3.3. Whittaker functions on G3 = GL(3; R) at the multiplicity one K3-types; 4. Whittaker functions on G3 = GL(3; C); 4.1. Irreducible representations of K3 = U(3) 4.2. Whittaker functions on G3 = GL(3 C) at the minimal K3-types; 5. The archimedean local theory of the standard L-functions for GL(n1) GL(n2) (n1 > n2); 5.1. The local Langlands correspondence for GL(n) over R; 5.2. The local Langlands correspondence for GL(n) over C; 5.3. The archimedean zeta integrals for GL(n1) GL(n2) (n1 > n2); 6. Calculus of the archimedean zeta integrals; 6.1. The archimedean zeta integrals for GL(3) GL(1); 6.2. The proof of Theorem 6.1; 6.3. The archimedean zeta integrals for GL(3) GL(2); References Arithmetic properties of p-adic elliptic logarithmic functions Noriko Hirata-Kohno |
| Record Nr. | UNINA-9910778806903321 |
| Singapore ; ; Hackensack, N.J., : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometry and analysis of automorphic forms of several variables [[electronic resource] ] : proceedings of the international symposium in honor of Takayuki Oda on the occasion of his 60th birthday, Tokyo, Japan, 14-17 September, 2009 / / editors, Yoshinori Hamahata ... [et al.]
| Geometry and analysis of automorphic forms of several variables [[electronic resource] ] : proceedings of the international symposium in honor of Takayuki Oda on the occasion of his 60th birthday, Tokyo, Japan, 14-17 September, 2009 / / editors, Yoshinori Hamahata ... [et al.] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (388 p.) |
| Disciplina | 515.94 |
| Altri autori (Persone) |
OdaTakayuki
HamahataYoshinori |
| Collana | Series on number theory and its application |
| Soggetto topico |
Geometry
Automorphic forms |
| ISBN |
1-280-37603-1
9786613555410 981-4355-60-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Program of symposium; Contents; The Birch and Swinnerton-Dyer conjecture for Q-curves and Oda's period relations Henri Darmon, Victor Rotger and Yu Zhao; 1. Introduction; 2. Background; 2.1. The Birch and Swinnerton-Dyer conjecture in low analytic rank; 2.2. Oda's period relations and ATR points; 3. The Birch and Swinnerton-Dyer conjecture for Q-curves; 3.1. Review of Q-curves; 3.2. The main result; 4. Heegner points on Shimura's elliptic curves; 4.1. An explicit Heegner point construction; 4.2. Heegner points and ATR cycles; 4.3. Numerical examples; 4.4. Proof of Proposition 4.1
ReferencesThe supremum of Newton polygons of p-divisible groups with a given p-kernel type Shushi Harashita; 1. Introduction; 2. A catalogue of p-divisible groups with a given type; 3. Preliminaries on F-zips; 4. Lifting of F-zips; 5. A reduction of the problem; 6. Extensions by a minimal p-divisible group; 7. Proof of Proposition 5.2; References; Borcherds lifts on Sp2(Z) Bernhard Heim and Atsushi Murase; 1. Introduction and the main results; 1.1. Introduction; 1.2. Siegel modular forms; 1.3. The organization of the paper; 1.4. Notation; 2. Borcherds lifts; 2.1. Jacobi forms 2.2. Humbert surfaces2.3. Siegel modular forms with a nontrivial character; 2.4. Borcherds lifts on; 2.5. Examples of Borcherds lifts; 3. Proof of the main results; 3.1. The multiplicative symmetry; 3.2. A characterization of powers of the modular discriminant; 3.3. The multiplicative symmetry for Sym2(Mk( 1)); 3.4. Proofs of Theorem 1.1 and Theorem 1.2 (i); 4. The weight formula; 4.1. Cohen numbers; 4.2. The weight formula for Borcherds lifts; Acknowledgement; References; The archimedean Whittaker functions on GL(3) Miki Hirano, Taku Ishii and Tadashi Miyazaki; 1. Introduction 2. Preliminaries2.1. Notation; 2.2. Basic objects; 2.3. Whittaker functions on Gn; 2.5. The contragradient Whittaker functions; 2.6. The generalized principal series representations of Gn = GL(n; R); 2.7. The principal series representations of Gn = GL(n; C); 3. Whittaker functions on G3 = GL(3; R); 3.1. Irreducible representations of K3 = O(3); 3.2. Whittaker functions on G3 = GL(3; R) at the minimal K3-types; 3.3. Whittaker functions on G3 = GL(3; R) at the multiplicity one K3-types; 4. Whittaker functions on G3 = GL(3; C); 4.1. Irreducible representations of K3 = U(3) 4.2. Whittaker functions on G3 = GL(3 C) at the minimal K3-types; 5. The archimedean local theory of the standard L-functions for GL(n1) GL(n2) (n1 > n2); 5.1. The local Langlands correspondence for GL(n) over R; 5.2. The local Langlands correspondence for GL(n) over C; 5.3. The archimedean zeta integrals for GL(n1) GL(n2) (n1 > n2); 6. Calculus of the archimedean zeta integrals; 6.1. The archimedean zeta integrals for GL(3) GL(1); 6.2. The proof of Theorem 6.1; 6.3. The archimedean zeta integrals for GL(3) GL(2); References Arithmetic properties of p-adic elliptic logarithmic functions Noriko Hirata-Kohno |
| Record Nr. | UNINA-9910821506503321 |
| Singapore ; ; Hackensack, N.J., : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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 genere / forma | Electronic books. |
| 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-9910453331303321 |
Yuan Xinyi <1981->
|
||
| Princeton, : Princeton University Press, 2012, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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 |
|
Yuan Xinyi <1981->
|
||
| Princeton, : Princeton University Press, 2012, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Gross-Zagier formula on Shimura curves / / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang
| The Gross-Zagier formula on Shimura curves / / 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-9910817785603321 |
|
Yuan Xinyi <1981->
|
||
| Princeton, : Princeton University Press, 2012, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Groups acting on hyperbolic space : harmonic analysis and number theory / J. Elstrodt, F. Grunewald, J. Mennicke
| Groups acting on hyperbolic space : harmonic analysis and number theory / J. Elstrodt, F. Grunewald, J. Mennicke |
| Autore | Elstrodt, Jürgen |
| Pubbl/distr/stampa | Berlin : Springer, c1998 |
| Descrizione fisica | xv, 524 p. ; 25 cm. |
| Disciplina | 512.7 |
| Altri autori (Persone) |
Grunewald, Fritz
Mennicke, Jens L. |
| Collana | Springer monographs in mathematics |
| Soggetto topico |
Spectral theory (Mathematics)
Selberg trace formula Automorphic forms Zeta functions Spectral theory |
| ISBN | 3540627456 |
| Classificazione |
LC QA320.E47
AMS 11F72 AMS 11F55 AMS 11E39 AMS 11E45 AMS 11M26 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991004040589707536 |
|
Elstrodt, Jürgen
|
||
| Berlin : Springer, c1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Harmonic analysis, group representations, automorphic forms, and invariant theory [[electronic resource] ] : in honor of Roger E. Howe / / editors, Jian-Shu Li
| Harmonic analysis, group representations, automorphic forms, and invariant theory [[electronic resource] ] : in honor of Roger E. Howe / / editors, Jian-Shu Li |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, 2007 |
| Descrizione fisica | 1 online resource (448 p.) |
| Disciplina | 515.2433 |
| Altri autori (Persone) |
HoweRoger
LiJian-Shu |
| Collana | Lecture notes series / Institute for Mathematical Sciences, National University of Singapore |
| Soggetto topico |
Symmetry (Mathematics)
Harmonic analysis Representations of groups Automorphic forms |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-91159-3
9786611911591 981-277-079-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS; Foreword; Preface; The Theta Correspondence over R Jeffrey Adams; 1. Introduction; 2. Fock Model: Complex Lie Algebra; 3. Schrodinger Model; 4. Fock Model: Real Lie Algebra; 5. Duality; 6. Compact Dual Pairs; 7. Joint Harmonics; 8. Induction Principle; 9. Examples; References; The Heisenberg Group, SL(3; R), and Rigidity Andreas Cap, Michael G. Cowling, Filippo De Mari, Michael Eastwood and Rupert McCallum; 1. Introduction; 2. An Example; 3. Related Questions in Two Dimensions; 4. Proof of Theorem 2.1; 5. Final Remarks; References
Pfafflans and Strategies for Integer Choice Games Ron Evans and Nolan Wallach1. Introduction; 2. Strategies for the Multivariate Game; 3. Strategies for the Single Variable Game; 4. Strategies for Some Constricted Multivariate Games; 5. Appendix: Pfa ans Associated with Payo Matrices; References; When is an L-Function Non-Vanishing in Part of the Critical Strip? Stephen Gelbart; Introduction; 1. The Classical Method; 2. The Rankin-Selberg Generalization of de la Vall ee Poussin; 3. An Approach Using Eisenstein Series on SL(2; R); 4. The General Method; References Cohomological Automorphic Forms on Unitary Groups, II: Period Relations and Values of L-Functions Michael HarrisIntroduction; Errors and Misprints in [H4]; 0. Preliminary Notation; 1. Eisenstein Series on Unitary Similitude Groups; 2. The Local Theta Correspondence; Appendix. Generic Calculation of the Unrami ed Correspondence; 3. Applications to Special Values of L-Functions; 4. Applications to Period Relations; The Inversion Formula and Holomorphic Extension of the Minimal Representation of the Conformal Group Toshiyuki Kobayashi and Gen Mano; Contents; 1. Introduction 1.1. Semigroup generated by a differential operator D1.2. Comparison with the Hermite operator D; 1.3. The action of SL(2; R) O(m); 1.4. Minimal representation as hidden symmetry; 2. Preliminary Results on the Minimal Representation of O(m + 1; 2); 2.1. Maximal parabolic subgroup of the conformal group; 2.2. L2-model of the minimal representation; 2.3. K-type decomposition; 2.4. Infinitesimal action of the minimal representation; 3. Branching Law of +; 3.1. Schr odinger model of the minimal representation; 3.2. K- nite functions on the forward light cone C+ 3.3. Description of in nitesimal generators of sl(2R); 3.4. Central element Z of kC; 3.5. Proof of Proposition 3.2.1; 3.6. One parameter holomorphic semigroup (etZ ); 4. Radial Part of the Semigroup; 4.1. Result of the section; 4.2. Upper estimate of the kernel function; 4.3. Proof of Theorem 4.1.1 (Case Re t > 0); 4.4. Proof of Theorem 4.1.1 (Case Re t = 0); 4.5. Weber's second exponential integral formula; 4.6. Dirac sequence operators; 5. Integral Formula for the Semigroup; 5.1. Result of the section; 5.2. Upper estimates of the kernel function 5.3. Proof of Theorem 5.1.1 (Case Re t > 0) |
| Record Nr. | UNINA-9910451141803321 |
| Singapore ; ; Hackensack, N.J., : World Scientific, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Harmonic analysis, group representations, automorphic forms, and invariant theory [[electronic resource] ] : in honor of Roger E. Howe / / editors, Jian-Shu Li
| Harmonic analysis, group representations, automorphic forms, and invariant theory [[electronic resource] ] : in honor of Roger E. Howe / / editors, Jian-Shu Li |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, 2007 |
| Descrizione fisica | 1 online resource (448 p.) |
| Disciplina | 515.2433 |
| Altri autori (Persone) |
HoweRoger
LiJian-Shu |
| Collana | Lecture notes series / Institute for Mathematical Sciences, National University of Singapore |
| Soggetto topico |
Symmetry (Mathematics)
Harmonic analysis Representations of groups Automorphic forms |
| ISBN |
1-281-91159-3
9786611911591 981-277-079-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS; Foreword; Preface; The Theta Correspondence over R Jeffrey Adams; 1. Introduction; 2. Fock Model: Complex Lie Algebra; 3. Schrodinger Model; 4. Fock Model: Real Lie Algebra; 5. Duality; 6. Compact Dual Pairs; 7. Joint Harmonics; 8. Induction Principle; 9. Examples; References; The Heisenberg Group, SL(3; R), and Rigidity Andreas Cap, Michael G. Cowling, Filippo De Mari, Michael Eastwood and Rupert McCallum; 1. Introduction; 2. An Example; 3. Related Questions in Two Dimensions; 4. Proof of Theorem 2.1; 5. Final Remarks; References
Pfafflans and Strategies for Integer Choice Games Ron Evans and Nolan Wallach1. Introduction; 2. Strategies for the Multivariate Game; 3. Strategies for the Single Variable Game; 4. Strategies for Some Constricted Multivariate Games; 5. Appendix: Pfa ans Associated with Payo Matrices; References; When is an L-Function Non-Vanishing in Part of the Critical Strip? Stephen Gelbart; Introduction; 1. The Classical Method; 2. The Rankin-Selberg Generalization of de la Vall ee Poussin; 3. An Approach Using Eisenstein Series on SL(2; R); 4. The General Method; References Cohomological Automorphic Forms on Unitary Groups, II: Period Relations and Values of L-Functions Michael HarrisIntroduction; Errors and Misprints in [H4]; 0. Preliminary Notation; 1. Eisenstein Series on Unitary Similitude Groups; 2. The Local Theta Correspondence; Appendix. Generic Calculation of the Unrami ed Correspondence; 3. Applications to Special Values of L-Functions; 4. Applications to Period Relations; The Inversion Formula and Holomorphic Extension of the Minimal Representation of the Conformal Group Toshiyuki Kobayashi and Gen Mano; Contents; 1. Introduction 1.1. Semigroup generated by a differential operator D1.2. Comparison with the Hermite operator D; 1.3. The action of SL(2; R) O(m); 1.4. Minimal representation as hidden symmetry; 2. Preliminary Results on the Minimal Representation of O(m + 1; 2); 2.1. Maximal parabolic subgroup of the conformal group; 2.2. L2-model of the minimal representation; 2.3. K-type decomposition; 2.4. Infinitesimal action of the minimal representation; 3. Branching Law of +; 3.1. Schr odinger model of the minimal representation; 3.2. K- nite functions on the forward light cone C+ 3.3. Description of in nitesimal generators of sl(2R); 3.4. Central element Z of kC; 3.5. Proof of Proposition 3.2.1; 3.6. One parameter holomorphic semigroup (etZ ); 4. Radial Part of the Semigroup; 4.1. Result of the section; 4.2. Upper estimate of the kernel function; 4.3. Proof of Theorem 4.1.1 (Case Re t > 0); 4.4. Proof of Theorem 4.1.1 (Case Re t = 0); 4.5. Weber's second exponential integral formula; 4.6. Dirac sequence operators; 5. Integral Formula for the Semigroup; 5.1. Result of the section; 5.2. Upper estimates of the kernel function 5.3. Proof of Theorem 5.1.1 (Case Re t > 0) |
| Record Nr. | UNINA-9910784809303321 |
| Singapore ; ; Hackensack, N.J., : World Scientific, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Harmonic analysis, group representations, automorphic forms, and invariant theory [[electronic resource] ] : in honor of Roger E. Howe / / editors, Jian-Shu Li
| Harmonic analysis, group representations, automorphic forms, and invariant theory [[electronic resource] ] : in honor of Roger E. Howe / / editors, Jian-Shu Li |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, 2007 |
| Descrizione fisica | 1 online resource (448 p.) |
| Disciplina | 515.2433 |
| Altri autori (Persone) |
HoweRoger
LiJian-Shu |
| Collana | Lecture notes series / Institute for Mathematical Sciences, National University of Singapore |
| Soggetto topico |
Symmetry (Mathematics)
Harmonic analysis Representations of groups Automorphic forms |
| ISBN |
1-281-91159-3
9786611911591 981-277-079-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS; Foreword; Preface; The Theta Correspondence over R Jeffrey Adams; 1. Introduction; 2. Fock Model: Complex Lie Algebra; 3. Schrodinger Model; 4. Fock Model: Real Lie Algebra; 5. Duality; 6. Compact Dual Pairs; 7. Joint Harmonics; 8. Induction Principle; 9. Examples; References; The Heisenberg Group, SL(3; R), and Rigidity Andreas Cap, Michael G. Cowling, Filippo De Mari, Michael Eastwood and Rupert McCallum; 1. Introduction; 2. An Example; 3. Related Questions in Two Dimensions; 4. Proof of Theorem 2.1; 5. Final Remarks; References
Pfafflans and Strategies for Integer Choice Games Ron Evans and Nolan Wallach1. Introduction; 2. Strategies for the Multivariate Game; 3. Strategies for the Single Variable Game; 4. Strategies for Some Constricted Multivariate Games; 5. Appendix: Pfa ans Associated with Payo Matrices; References; When is an L-Function Non-Vanishing in Part of the Critical Strip? Stephen Gelbart; Introduction; 1. The Classical Method; 2. The Rankin-Selberg Generalization of de la Vall ee Poussin; 3. An Approach Using Eisenstein Series on SL(2; R); 4. The General Method; References Cohomological Automorphic Forms on Unitary Groups, II: Period Relations and Values of L-Functions Michael HarrisIntroduction; Errors and Misprints in [H4]; 0. Preliminary Notation; 1. Eisenstein Series on Unitary Similitude Groups; 2. The Local Theta Correspondence; Appendix. Generic Calculation of the Unrami ed Correspondence; 3. Applications to Special Values of L-Functions; 4. Applications to Period Relations; The Inversion Formula and Holomorphic Extension of the Minimal Representation of the Conformal Group Toshiyuki Kobayashi and Gen Mano; Contents; 1. Introduction 1.1. Semigroup generated by a differential operator D1.2. Comparison with the Hermite operator D; 1.3. The action of SL(2; R) O(m); 1.4. Minimal representation as hidden symmetry; 2. Preliminary Results on the Minimal Representation of O(m + 1; 2); 2.1. Maximal parabolic subgroup of the conformal group; 2.2. L2-model of the minimal representation; 2.3. K-type decomposition; 2.4. Infinitesimal action of the minimal representation; 3. Branching Law of +; 3.1. Schr odinger model of the minimal representation; 3.2. K- nite functions on the forward light cone C+ 3.3. Description of in nitesimal generators of sl(2R); 3.4. Central element Z of kC; 3.5. Proof of Proposition 3.2.1; 3.6. One parameter holomorphic semigroup (etZ ); 4. Radial Part of the Semigroup; 4.1. Result of the section; 4.2. Upper estimate of the kernel function; 4.3. Proof of Theorem 4.1.1 (Case Re t > 0); 4.4. Proof of Theorem 4.1.1 (Case Re t = 0); 4.5. Weber's second exponential integral formula; 4.6. Dirac sequence operators; 5. Integral Formula for the Semigroup; 5.1. Result of the section; 5.2. Upper estimates of the kernel function 5.3. Proof of Theorem 5.1.1 (Case Re t > 0) |
| Record Nr. | UNINA-9910820121903321 |
| Singapore ; ; Hackensack, N.J., : World Scientific, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Soggetto topico
-
Automorphic forms
(127)
- Representations of groups (33)
- L-functions (22)
- Discontinuous groups (16)
- Automorphic functions (12)