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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 : how one can compute in polynomial time the value of Ramanujan's tau at a prime / edited by Bas Edixhoven and Jean-Marc Couveignes
| Computational aspects of modular forms and Galois representations : how one can compute in polynomial time the value of Ramanujan's tau at a prime / edited by Bas Edixhoven and Jean-Marc Couveignes |
| Pubbl/distr/stampa | Princeton : Princeton University Press, c2011 |
| Descrizione fisica | xi, 425 p. ; 25 cm |
| Disciplina | 512.32 |
| Altri autori (Persone) |
Edixhoven, Bas
Couveignes, Jean-Marc |
| Collana | Annals of mathematics studies ; 176 |
| Soggetto topico |
Galois modules (Algebra)
Class field theory |
| ISBN |
9780691142012
9780691142029 |
| Classificazione |
AMS 11-06
AMS 11F03 AMS 00B15 LC QA247.C638 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001370519707536 |
| Princeton : Princeton University Press, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
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 | ||
| ||
Galois module structure / Victor P. Snaith
| Galois module structure / Victor P. Snaith |
| Autore | Snaith, Victor Percy |
| Pubbl/distr/stampa | Providence, R. I. : American Mathematical Society, 1994 |
| Descrizione fisica | vii, 207 p. ; 27 cm |
| Disciplina | 512.74 |
| Collana | Fields Institute monographs, 1069-5273 ; 2 |
| Soggetto topico |
Galois modules (Algebra)
L-functions |
| ISBN | 082180264X |
| Classificazione |
AMS 11M06
AMS 11R23 AMS 11R33 AMS 11R34 AMS 11R65 AMS 11R70 AMS 11S25 AMS 11S31 AMS 11S40 AMS 12G05 AMS 16G99 AMS 16H05 AMS 19A31 AMS 19D99 AMS 19F27 AMS 20J06 QA247.S497 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000925599707536 |
Snaith, Victor Percy
|
||
| Providence, R. I. : American Mathematical Society, 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
The lifted root number conjecture and Iwasawa theory / / Jürgen Ritter, Alfred Weiss
| The lifted root number conjecture and Iwasawa theory / / Jürgen Ritter, Alfred Weiss |
| Autore | Ritter J (Jürgen), <1943-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2002] |
| Descrizione fisica | 1 online resource (105 p.) |
| Disciplina |
510 s
512/.74 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Iwasawa theory
Galois modules (Algebra) L-functions Class field theory |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0341-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Table of Contents""; ""1. Introduction""; ""2. The Tripod""; ""3. Restriction, deflation; change of maps, and variance with S""; ""4. Definition of [omitted][sub(s)] ; Ω[sub(Î?)] as a shadow of [omitted][sub(s)]""; ""5. [omitted][sub(s)] over the maximal order in the case when G is abelian""; ""6. Local considerations""; ""7. Towards a representing homomorphism for Ω[sub([omitted]L)]""; ""8. Real cyclotomic extensions tame over l""; ""References"" |
| Record Nr. | UNINA-9910480871503321 |
|
Ritter J (Jürgen), <1943->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2002] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The lifted root number conjecture and Iwasawa theory / / Jürgen Ritter, Alfred Weiss
| The lifted root number conjecture and Iwasawa theory / / Jürgen Ritter, Alfred Weiss |
| Autore | Ritter J (Jürgen), <1943-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2002] |
| Descrizione fisica | 1 online resource (105 p.) |
| Disciplina |
510 s
512/.74 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Iwasawa theory
Galois modules (Algebra) L-functions Class field theory |
| ISBN | 1-4704-0341-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Table of Contents""; ""1. Introduction""; ""2. The Tripod""; ""3. Restriction, deflation; change of maps, and variance with S""; ""4. Definition of [omitted][sub(s)] ; Ω[sub(Î?)] as a shadow of [omitted][sub(s)]""; ""5. [omitted][sub(s)] over the maximal order in the case when G is abelian""; ""6. Local considerations""; ""7. Towards a representing homomorphism for Ω[sub([omitted]L)]""; ""8. Real cyclotomic extensions tame over l""; ""References"" |
| Record Nr. | UNINA-9910788846703321 |
|
Ritter J (Jürgen), <1943->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2002] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The lifted root number conjecture and Iwasawa theory / / Jürgen Ritter, Alfred Weiss
| The lifted root number conjecture and Iwasawa theory / / Jürgen Ritter, Alfred Weiss |
| Autore | Ritter J (Jürgen), <1943-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2002] |
| Descrizione fisica | 1 online resource (105 p.) |
| Disciplina |
510 s
512/.74 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Iwasawa theory
Galois modules (Algebra) L-functions Class field theory |
| ISBN | 1-4704-0341-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Table of Contents""; ""1. Introduction""; ""2. The Tripod""; ""3. Restriction, deflation; change of maps, and variance with S""; ""4. Definition of [omitted][sub(s)] ; Ω[sub(Î?)] as a shadow of [omitted][sub(s)]""; ""5. [omitted][sub(s)] over the maximal order in the case when G is abelian""; ""6. Local considerations""; ""7. Towards a representing homomorphism for Ω[sub([omitted]L)]""; ""8. Real cyclotomic extensions tame over l""; ""References"" |
| Record Nr. | UNINA-9910818970803321 |
|
Ritter J (Jürgen), <1943->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2002] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The second Chinburg conjecture for quaternion fields / / Jeff Hooper, Victor Snaith, Minh van Tran
| The second Chinburg conjecture for quaternion fields / / Jeff Hooper, Victor Snaith, Minh van Tran |
| Autore | Hooper Jeff <1968-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (146 p.) |
| Disciplina |
510 s
512/.74 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Galois modules (Algebra)
Quaternions |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0295-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Chapter 1. Class-groups of group-rings""; ""1. Hom Descriptions""; ""2. The class-group of Z[Q[sub(8)]]""; ""3. The second Chinburg conjecture""; ""Chapter 2. The evaluation of [X]""; ""1. A Hom-description representative of [X]""; ""2. Kim's Examples""; ""Chapter 3. Quaternion fields over Q[sub(2)]""; ""1. Galois actions""; ""2. Fundamental 2-extensions""; ""3. The fundamental 2-extension in Case A""; ""4. The fundamental 2-extension in Case B""; ""5. The fundamental 2-extension in Case C""; ""Chapter 4. The Invariant in Cases A, B and C""
""1. The strategy of the calculation""""2. Evaluating [Ker(k')] in Case A""; ""3. Evaluating [Ker(k')] in Case B""; ""4. Evaluating [Ker(k')] in Case C""; ""Chapter 5. The evaluation of [M]""; ""1. The class [M] in Case A""; ""2. The class [M] in Case B""; ""3. The class [M] in Case C""; ""Chapter 6. The conjecture in Cases A, B and C""; ""1. Evaluation of [X] in Cases A, B and C""; ""2. The proof in Cases A, B and C""; ""Chapter 7. Epilogue""; ""1. Related and Subsequent Results""; ""Bibliography""; ""Index"" |
| Record Nr. | UNINA-9910479989103321 |
|
Hooper Jeff <1968->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The second Chinburg conjecture for quaternion fields / / Jeff Hooper, Victor Snaith, Minh van Tran
| The second Chinburg conjecture for quaternion fields / / Jeff Hooper, Victor Snaith, Minh van Tran |
| Autore | Hooper Jeff <1968-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (146 p.) |
| Disciplina |
510 s
512/.74 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Galois modules (Algebra)
Quaternions |
| ISBN | 1-4704-0295-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Chapter 1. Class-groups of group-rings""; ""1. Hom Descriptions""; ""2. The class-group of Z[Q[sub(8)]]""; ""3. The second Chinburg conjecture""; ""Chapter 2. The evaluation of [X]""; ""1. A Hom-description representative of [X]""; ""2. Kim's Examples""; ""Chapter 3. Quaternion fields over Q[sub(2)]""; ""1. Galois actions""; ""2. Fundamental 2-extensions""; ""3. The fundamental 2-extension in Case A""; ""4. The fundamental 2-extension in Case B""; ""5. The fundamental 2-extension in Case C""; ""Chapter 4. The Invariant in Cases A, B and C""
""1. The strategy of the calculation""""2. Evaluating [Ker(k')] in Case A""; ""3. Evaluating [Ker(k')] in Case B""; ""4. Evaluating [Ker(k')] in Case C""; ""Chapter 5. The evaluation of [M]""; ""1. The class [M] in Case A""; ""2. The class [M] in Case B""; ""3. The class [M] in Case C""; ""Chapter 6. The conjecture in Cases A, B and C""; ""1. Evaluation of [X] in Cases A, B and C""; ""2. The proof in Cases A, B and C""; ""Chapter 7. Epilogue""; ""1. Related and Subsequent Results""; ""Bibliography""; ""Index"" |
| Record Nr. | UNINA-9910788842303321 |
|
Hooper Jeff <1968->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The second Chinburg conjecture for quaternion fields / / Jeff Hooper, Victor Snaith, Minh van Tran
| The second Chinburg conjecture for quaternion fields / / Jeff Hooper, Victor Snaith, Minh van Tran |
| Autore | Hooper Jeff <1968-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (146 p.) |
| Disciplina |
510 s
512/.74 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Galois modules (Algebra)
Quaternions |
| ISBN | 1-4704-0295-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Chapter 1. Class-groups of group-rings""; ""1. Hom Descriptions""; ""2. The class-group of Z[Q[sub(8)]]""; ""3. The second Chinburg conjecture""; ""Chapter 2. The evaluation of [X]""; ""1. A Hom-description representative of [X]""; ""2. Kim's Examples""; ""Chapter 3. Quaternion fields over Q[sub(2)]""; ""1. Galois actions""; ""2. Fundamental 2-extensions""; ""3. The fundamental 2-extension in Case A""; ""4. The fundamental 2-extension in Case B""; ""5. The fundamental 2-extension in Case C""; ""Chapter 4. The Invariant in Cases A, B and C""
""1. The strategy of the calculation""""2. Evaluating [Ker(k')] in Case A""; ""3. Evaluating [Ker(k')] in Case B""; ""4. Evaluating [Ker(k')] in Case C""; ""Chapter 5. The evaluation of [M]""; ""1. The class [M] in Case A""; ""2. The class [M] in Case B""; ""3. The class [M] in Case C""; ""Chapter 6. The conjecture in Cases A, B and C""; ""1. Evaluation of [X] in Cases A, B and C""; ""2. The proof in Cases A, B and C""; ""Chapter 7. Epilogue""; ""1. Related and Subsequent Results""; ""Bibliography""; ""Index"" |
| Record Nr. | UNINA-9910818133403321 |
|
Hooper Jeff <1968->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Soggetto topico
-
Galois modules (Algebra)
(11)
- Class field theory (6)
- L-functions (4)
- Iwasawa theory (3)
- Quaternions (3)