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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 | ||
| ||
Fourier Coefficients of Automorphic Forms / Roelof W. Bruggeman
| Fourier Coefficients of Automorphic Forms / Roelof W. Bruggeman |
| Autore | Bruggeman, Roelof W. |
| Pubbl/distr/stampa | Berlin, : Springer, 1981 |
| Descrizione fisica | vi, 206 p. ; 24 cm |
| Soggetto non controllato |
Automorphic forms
Coefficients Convolution Fourier Fourier coefficients Groups Models Presentation Scala Shapes Spectral Theorem |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0261810 |
Bruggeman, Roelof W.
|
||
| Berlin, : Springer, 1981 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Fourier Coefficients of Automorphic Forms / Roelof W. Bruggeman
| Fourier Coefficients of Automorphic Forms / Roelof W. Bruggeman |
| Autore | Bruggeman, Roelof W. |
| Pubbl/distr/stampa | Berlin, : Springer, 1981 |
| Descrizione fisica | vi, 206 p. ; 24 cm |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
11F12 - Automorphic forms, one variable [MSC 2020] 11F70 - Representation-theoretic methods; automorphic representations over local and global fields [MSC 2020] 22E40 - Discrete subgroups of Lie groups [MSC 2020] 30F25 - Ideal boundary theory for Riemann surfaces [MSC 2020] 43A65 - Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) [MSC 2020] |
| Soggetto non controllato |
Automorphic forms
Coefficients Convolution Fourier Fourier coefficients Groups Models Presentations Scala Shapes Spectral Theorem |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN00261810 |
|
Bruggeman, Roelof W.
|
||
| Berlin, : Springer, 1981 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Siegel Modular Forms : A Classical and Representation-Theoretic Approach / Ameya Pitale
| Siegel Modular Forms : A Classical and Representation-Theoretic Approach / Ameya Pitale |
| Autore | Pitale, Ameya |
| Pubbl/distr/stampa | Cham, : Springer, 2019 |
| Descrizione fisica | ix, 138 p. : ill. ; 24 cm |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
20-XX - Group theory and generalizations [MSC 2020] |
| Soggetto non controllato |
Automorphic representations
Deligne's conjecture Fermat's Last Theorem Fourier coefficients Hecke algebra L-functions Number theory Representation Theory Shimura-Taniyama-Weil conjecture Siegel modular forms Symplectic Groups |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN0125411 |
|
Pitale, Ameya
|
||
| Cham, : Springer, 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Siegel Modular Forms : A Classical and Representation-Theoretic Approach / Ameya Pitale
| Siegel Modular Forms : A Classical and Representation-Theoretic Approach / Ameya Pitale |
| Autore | Pitale, Ameya |
| Pubbl/distr/stampa | Cham, : Springer, 2019 |
| Descrizione fisica | ix, 138 p. : ill. ; 24 cm |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
20-XX - Group theory and generalizations [MSC 2020] |
| Soggetto non controllato |
Automorphic representations
Deligne's conjecture Fermat's Last Theorem Fourier coefficients Hecke algebra L-functions Number theory Representation Theory Shimura-Taniyama-Weil conjecture Siegel modular forms Symplectic Groups |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00125411 |
|
Pitale, Ameya
|
||
| Cham, : Springer, 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||