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Computational aspects of modular forms and Galois representations [[electronic resource] ] : how one can compute in polynomial time the value of Ramanujan's tau at a prime / / edited by Jean-Marc Couveignes and Bas Edixhoven
| Computational aspects of modular forms and Galois representations [[electronic resource] ] : how one can compute in polynomial time the value of Ramanujan's tau at a prime / / edited by Jean-Marc Couveignes and Bas Edixhoven |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, c2011 |
| Descrizione fisica | 1 online resource (438 p.) |
| Disciplina | 512/.32 |
| Altri autori (Persone) |
EdixhovenB <1962-> (Bas)
CouveignesJean-Marc |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Galois modules (Algebra)
Class field theory |
| Soggetto genere / forma | Electronic books. |
| Soggetto non controllato |
Arakelov invariants
Arakelov theory Fourier coefficients Galois representation Galois representations Green functions Hecke operators Jacobians Langlands program Las Vegas algorithm Lehmer Peter Bruin Ramanujan's tau function Ramanujan's tau-function Ramanujan's tau Riemann surfaces Schoof's algorithm Turing machines algorithms arithmetic geometry arithmetic surfaces bounding heights bounds coefficients complex roots computation computing algorithms computing coefficients cusp forms cuspidal divisor eigenforms finite fields height functions inequality lattices minimal polynomial modular curves modular forms modular representation modular representations modular symbols nonvanishing conjecture p-adic methods plane curves polynomial time algorithm polynomial time algoriths polynomial time polynomials power series probabilistic polynomial time random divisors residual representation square root square-free levels tale cohomology torsion divisors torsion |
| ISBN |
1-283-05180-X
9786613051806 1-4008-3900-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Acknowledgments -- Author information -- Dependencies between the chapters -- Chapter 1. Introduction, main results, context / Edixhoven, Bas -- Chapter 2. Modular curves, modular forms, lattices, Galois representations / Edixhoven, Bas -- Chapter 3. First description of the algorithms / Couveignes, Jean-Marc / Edixhoven, Bas -- Chapter 4. Short introduction to heights and Arakelov theory / Edixhoven, Bas / de Jong, Robin -- Chapter 5. Computing complex zeros of polynomials and power series / Couveignes, Jean-Marc -- Chapter 6. Computations with modular forms and Galois representations / Bosman, Johan -- Chapter 7. Polynomials for projective representations of level one forms / Bosman, Johan -- Chapter 8. Description of X1(5l) / Edixhoven, Bas -- Chapter 9. Applying Arakelov theory / Edixhoven, Bas / de Jong, Robin -- Chapter 10. An upper bound for Green functions on Riemann surfaces / Merkl, Franz -- Chapter 11. Bounds for Arakelov invariants of modular curves / Edixhoven, B. / de Jong, R. -- Chapter 12. Approximating Vf over the complex numbers / Couveignes, Jean-Marc -- Chapter 13. Computing Vf modulo p / Couveignes, Jean-Marc -- Chapter 14. Computing the residual Galois representations / Edixhoven, Bas -- Chapter 15. Computing coefficients of modular forms / Edixhoven, Bas -- Epilogue -- Bibliography -- Index |
| Record Nr. | UNINA-9910460447203321 |
| Princeton, N.J., : Princeton University Press, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computational aspects of modular forms and Galois representations [[electronic resource] ] : how one can compute in polynomial time the value of Ramanujan's tau at a prime / / edited by Jean-Marc Couveignes and Bas Edixhoven
| Computational aspects of modular forms and Galois representations [[electronic resource] ] : how one can compute in polynomial time the value of Ramanujan's tau at a prime / / edited by Jean-Marc Couveignes and Bas Edixhoven |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, c2011 |
| Descrizione fisica | 1 online resource (438 p.) |
| Disciplina | 512/.32 |
| Altri autori (Persone) |
EdixhovenB <1962-> (Bas)
CouveignesJean-Marc |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Galois modules (Algebra)
Class field theory |
| Soggetto non controllato |
Arakelov invariants
Arakelov theory Fourier coefficients Galois representation Galois representations Green functions Hecke operators Jacobians Langlands program Las Vegas algorithm Lehmer Peter Bruin Ramanujan's tau function Ramanujan's tau-function Ramanujan's tau Riemann surfaces Schoof's algorithm Turing machines algorithms arithmetic geometry arithmetic surfaces bounding heights bounds coefficients complex roots computation computing algorithms computing coefficients cusp forms cuspidal divisor eigenforms finite fields height functions inequality lattices minimal polynomial modular curves modular forms modular representation modular representations modular symbols nonvanishing conjecture p-adic methods plane curves polynomial time algorithm polynomial time algoriths polynomial time polynomials power series probabilistic polynomial time random divisors residual representation square root square-free levels tale cohomology torsion divisors torsion |
| ISBN |
1-283-05180-X
9786613051806 1-4008-3900-9 |
| Classificazione | MAT001000MAT012010 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Acknowledgments -- Author information -- Dependencies between the chapters -- Chapter 1. Introduction, main results, context / Edixhoven, Bas -- Chapter 2. Modular curves, modular forms, lattices, Galois representations / Edixhoven, Bas -- Chapter 3. First description of the algorithms / Couveignes, Jean-Marc / Edixhoven, Bas -- Chapter 4. Short introduction to heights and Arakelov theory / Edixhoven, Bas / de Jong, Robin -- Chapter 5. Computing complex zeros of polynomials and power series / Couveignes, Jean-Marc -- Chapter 6. Computations with modular forms and Galois representations / Bosman, Johan -- Chapter 7. Polynomials for projective representations of level one forms / Bosman, Johan -- Chapter 8. Description of X1(5l) / Edixhoven, Bas -- Chapter 9. Applying Arakelov theory / Edixhoven, Bas / de Jong, Robin -- Chapter 10. An upper bound for Green functions on Riemann surfaces / Merkl, Franz -- Chapter 11. Bounds for Arakelov invariants of modular curves / Edixhoven, B. / de Jong, R. -- Chapter 12. Approximating Vf over the complex numbers / Couveignes, Jean-Marc -- Chapter 13. Computing Vf modulo p / Couveignes, Jean-Marc -- Chapter 14. Computing the residual Galois representations / Edixhoven, Bas -- Chapter 15. Computing coefficients of modular forms / Edixhoven, Bas -- Epilogue -- Bibliography -- Index |
| Record Nr. | UNINA-9910789850303321 |
| Princeton, N.J., : Princeton University Press, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computational aspects of modular forms and Galois representations [[electronic resource] ] : how one can compute in polynomial time the value of Ramanujan's tau at a prime / / edited by Jean-Marc Couveignes and Bas Edixhoven
| Computational aspects of modular forms and Galois representations [[electronic resource] ] : how one can compute in polynomial time the value of Ramanujan's tau at a prime / / edited by Jean-Marc Couveignes and Bas Edixhoven |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, c2011 |
| Descrizione fisica | 1 online resource (438 p.) |
| Disciplina | 512/.32 |
| Altri autori (Persone) |
EdixhovenB <1962-> (Bas)
CouveignesJean-Marc |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Galois modules (Algebra)
Class field theory |
| Soggetto non controllato |
Arakelov invariants
Arakelov theory Fourier coefficients Galois representation Galois representations Green functions Hecke operators Jacobians Langlands program Las Vegas algorithm Lehmer Peter Bruin Ramanujan's tau function Ramanujan's tau-function Ramanujan's tau Riemann surfaces Schoof's algorithm Turing machines algorithms arithmetic geometry arithmetic surfaces bounding heights bounds coefficients complex roots computation computing algorithms computing coefficients cusp forms cuspidal divisor eigenforms finite fields height functions inequality lattices minimal polynomial modular curves modular forms modular representation modular representations modular symbols nonvanishing conjecture p-adic methods plane curves polynomial time algorithm polynomial time algoriths polynomial time polynomials power series probabilistic polynomial time random divisors residual representation square root square-free levels tale cohomology torsion divisors torsion |
| ISBN |
1-283-05180-X
9786613051806 1-4008-3900-9 |
| Classificazione | MAT001000MAT012010 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Acknowledgments -- Author information -- Dependencies between the chapters -- Chapter 1. Introduction, main results, context / Edixhoven, Bas -- Chapter 2. Modular curves, modular forms, lattices, Galois representations / Edixhoven, Bas -- Chapter 3. First description of the algorithms / Couveignes, Jean-Marc / Edixhoven, Bas -- Chapter 4. Short introduction to heights and Arakelov theory / Edixhoven, Bas / de Jong, Robin -- Chapter 5. Computing complex zeros of polynomials and power series / Couveignes, Jean-Marc -- Chapter 6. Computations with modular forms and Galois representations / Bosman, Johan -- Chapter 7. Polynomials for projective representations of level one forms / Bosman, Johan -- Chapter 8. Description of X1(5l) / Edixhoven, Bas -- Chapter 9. Applying Arakelov theory / Edixhoven, Bas / de Jong, Robin -- Chapter 10. An upper bound for Green functions on Riemann surfaces / Merkl, Franz -- Chapter 11. Bounds for Arakelov invariants of modular curves / Edixhoven, B. / de Jong, R. -- Chapter 12. Approximating Vf over the complex numbers / Couveignes, Jean-Marc -- Chapter 13. Computing Vf modulo p / Couveignes, Jean-Marc -- Chapter 14. Computing the residual Galois representations / Edixhoven, Bas -- Chapter 15. Computing coefficients of modular forms / Edixhoven, Bas -- Epilogue -- Bibliography -- Index |
| Record Nr. | UNINA-9910823671503321 |
| Princeton, N.J., : Princeton University Press, c2011 | ||
| 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 [[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-9910817785603321 |
|
Yuan Xinyi <1981->
|
||
| Princeton, : Princeton University Press, 2012, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 / / Gerd Faltings
| Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 / / Gerd Faltings |
| Autore | Faltings Gerd |
| Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
| Descrizione fisica | 1 online resource (113 pages) |
| Disciplina | 516.3/5 |
| Altri autori (Persone) | ZhangShouwu |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Geometry, Algebraic
Riemann-Roch theorems |
| Soggetto non controllato |
Addition
Adjoint Alexander Grothendieck Algebraic geometry Analytic torsion Arakelov theory Asymptote Asymptotic expansion Asymptotic formula Big O notation Cartesian coordinate system Characteristic class Chern class Chow group Closed immersion Codimension Coherent sheaf Cohomology Combination Commutator Computation Covariant derivative Curvature Derivative Determinant Diagonal Differentiable manifold Differential form Dimension (vector space) Divisor Domain of a function Dual basis E6 (mathematics) Eigenvalues and eigenvectors Embedding Endomorphism Exact sequence Exponential function Generic point Heat kernel Injective function Intersection theory K-group Levi-Civita connection Line bundle Linear algebra Local coordinates Mathematical induction Morphism Natural number Neighbourhood (mathematics) Parameter Projective space Pullback (category theory) Pullback (differential geometry) Pullback Riemannian manifold Riemann–Roch theorem Self-adjoint operator Smoothness Sobolev space Stochastic calculus Summation Supertrace Theorem Transition function Upper half-plane Vector bundle Volume form |
| ISBN | 1-4008-8247-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- LIST OF SYMBOLS -- LECTURE 1. CLASSICAL RIEMANN-ROCH THEOREM -- LECTURE 2. CHERN CLASSES OF ARITHMETIC VECTOR BUNDLES -- LECTURE 3. LAPLACIANS AND HEAT KERNELS -- LECTURE 4. THE LOCAL INDEX THEOREM FOR DIRAC OPERATORS -- LECTURE 5. NUMBER OPERATORS AND DIRECT IMAGES -- LECTURE 6. ARITHMETIC RIEMANN-ROCH THEOREM -- LECTURE 7. THE THEOREM OF BISMUT-VASSEROT -- REFERENCES |
| Record Nr. | UNINA-9910154744103321 |
|
Faltings Gerd
|
||
| Princeton, NJ : , : Princeton University Press, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||