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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
Opac: Controlla la disponibilità qui
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
Opac: Controlla la disponibilità qui
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 Jean-Marc Couveignes and Bas Edixhoven
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 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
Opac: Controlla la disponibilità qui