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Arithmetic Geometry, Number Theory, and Computation / Jennifer S. Balakrishnan ... [et al.] editors
| Arithmetic Geometry, Number Theory, and Computation / Jennifer S. Balakrishnan ... [et al.] editors |
| Pubbl/distr/stampa | Cham, : Springer, 2021 |
| Descrizione fisica | x, 587 p. : ill. ; 24 cm |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
11Yxx - Computational number theory [MSC 2020] 11Gxx - Arithmetic algebraic geometry (Diophantine geometry) [MSC 2020] 14H40 - Jacobians, Prym varieties [MSC 2020] |
| Soggetto non controllato |
Birch-Swinnerton-Dyer conjecture
Chabauty–Coleman method Elliptic curves Galois groups Hecke operators Hilbert modular forms Hypersymmetric Abelian varieties Jacobians Subgroups Weil polynomials Zeta functions |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0274579 |
| Cham, : Springer, 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Arithmetic Geometry, Number Theory, and Computation / Jennifer S. Balakrishnan ... [et al.] editors
| Arithmetic Geometry, Number Theory, and Computation / Jennifer S. Balakrishnan ... [et al.] editors |
| Pubbl/distr/stampa | Cham, : Springer, 2021 |
| Descrizione fisica | x, 587 p. : ill. ; 24 cm |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
11Gxx - Arithmetic algebraic geometry (Diophantine geometry) [MSC 2020] 11Yxx - Computational number theory [MSC 2020] 14H40 - Jacobians, Prym varieties [MSC 2020] |
| Soggetto non controllato |
Birch-Swinnerton-Dyer conjecture
Chabauty–Coleman method Elliptic curves Galois groups Hecke operators Hilbert modular forms Hypersymmetric Abelian varieties Jacobians Subgroups Weil polynomials Zeta functions |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN00274579 |
| Cham, : Springer, 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
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 | ||
| ||
Directions in number theory : proceedings of the 2014 WIN3 workshop / Ellen E. Eischen ... [et al.] editors
| Directions in number theory : proceedings of the 2014 WIN3 workshop / Ellen E. Eischen ... [et al.] editors |
| Pubbl/distr/stampa | [Cham], : Springer, 2016 |
| Descrizione fisica | XV, 339 p. : ill. ; 24 cm |
| Soggetto topico |
11-XX - Number theory [MSC 2020]
11Rxx - Algebraic number theory: global fields [MSC 2020] 11T71 Algebraic coding theory; cryptography [MSC 2020] 00B25 - Proceedings of conferences of miscellaneous specific interest [MSC 2020] 11F70 - Representation-theoretic methods; automorphic representations over local and global fields [MSC 2020] 11Gxx - Arithmetic algebraic geometry (Diophantine geometry) [MSC 2020] 33C05 - Classical hypergeometric functions, ${}_2F_1$ [MSC 2020] 94B05 - Linear codes, general [MSC 2020] 11D41 - Higher degree equations; Fermat's equation [MSC 2020] |
| Soggetto non controllato |
Algebraic number theory
Analytic Number Theory Applied number theory Arithmetic Geometry Arithmetic of curves Cryptography Elliptic curves Galois theory Hecke operators P-adic automorphic forms Rational points on varieties via cohomological methods Rational points over number fields Shimura curves |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN0114637 |
| [Cham], : Springer, 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Directions in number theory : proceedings of the 2014 WIN3 workshop / Ellen E. Eischen ... [et al.] editors
| Directions in number theory : proceedings of the 2014 WIN3 workshop / Ellen E. Eischen ... [et al.] editors |
| Pubbl/distr/stampa | [Cham], : Springer, 2016 |
| Descrizione fisica | XV, 339 p. : ill. ; 24 cm |
| Soggetto topico |
00B25 - Proceedings of conferences of miscellaneous specific interest [MSC 2020]
11-XX - Number theory [MSC 2020] 11D41 - Higher degree equations; Fermat's equation [MSC 2020] 11F70 - Representation-theoretic methods; automorphic representations over local and global fields [MSC 2020] 11Gxx - Arithmetic algebraic geometry (Diophantine geometry) [MSC 2020] 11Rxx - Algebraic number theory: global fields [MSC 2020] 11T71 Algebraic coding theory; cryptography [MSC 2020] 33C05 - Classical hypergeometric functions, ${}_2F_1$ [MSC 2020] 94B05 - Linear codes, general [MSC 2020] |
| Soggetto non controllato |
Algebraic number theory
Analytic Number Theory Applied number theory Arithmetic Geometry Arithmetic of curves Cryptography Elliptic curves Galois theory Hecke operators P-adic automorphic forms Rational points on varieties via cohomological methods Rational points over number fields Shimura curves |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00114637 |
| [Cham], : Springer, 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||