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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
Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
Autore Katz Nicholas M. <1943->
Edizione [Course Book]
Pubbl/distr/stampa Princeton ; ; Oxford, : Princeton University Press, c2012
Descrizione fisica 1 online resource (213 p.)
Disciplina 515/.723
Collana Annals of mathematics studies
Soggetto topico Mellin transform
Convolutions (Mathematics)
Sequences (Mathematics)
Soggetto non controllato ArtinГchreier reduced polynomial
Emanuel Kowalski
EulerАoincar formula
Frobenius conjugacy class
Frobenius conjugacy
Frobenius tori
GoursatЋolchinВibet theorem
Kloosterman sheaf
Laurent polynomial
Legendre
Mellin transform
Pierre Deligne
Ron Evans
Tannakian category
Tannakian groups
Zeeev Rudnick
algebro-geometric
autodual objects
autoduality
characteristic two
connectedness
dimensional objects
duality
equidistribution
exponential sums
fiber functor
finite field Mellin transform
finite field
finite fields
geometrical irreducibility
group scheme
hypergeometric sheaf
interger monic polynomials
isogenies
lie-irreducibility
lisse
middle convolution
middle extension sheaf
monic polynomial
monodromy groups
noetherian connected scheme
nonsplit form
nontrivial additive character
number theory
odd characteristic
odd prime
orthogonal case
perverse sheaves
polynomials
pure weight
semisimple object
semisimple
sheaves
signs
split form
supermorse
theorem
theorems
ISBN 1-283-37996-1
9786613379962
1-4008-4270-0
Classificazione SI 830
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front matter -- Contents -- Introduction -- CHAPTER 1. Overview -- CHAPTER 2. Convolution of Perverse Sheaves -- CHAPTER 3. Fibre Functors -- CHAPTER 4. The Situation over a Finite Field -- CHAPTER 5. Frobenius Conjugacy Classes -- CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith -- CHAPTER 7. The Main Theorem -- CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility -- CHAPTER 9. Autodualities and Signs -- CHAPTER 10. A First Construction of Autodual Objects -- CHAPTER 11. A Second Construction of Autodual Objects -- CHAPTER 12. The Previous Construction in the Nonsplit Case -- CHAPTER 13. Results of Goursat-Kolchin-Ribet Type -- CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick -- CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family -- CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith -- CHAPTER 17. GL(n) Examples -- CHAPTER 18. Symplectic Examples -- CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples -- CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples -- CHAPTER 21. SL(n) Examples, for n an Odd Prime -- CHAPTER 22. SL(n) Examples with Slightly Composite n -- CHAPTER 23. Other SL(n) Examples -- CHAPTER 24. An O(2n) Example -- CHAPTER 25. G2 Examples: the Overall Strategy -- CHAPTER 26. G2 Examples: Construction in Characteristic Two -- CHAPTER 27. G2 Examples: Construction in Odd Characteristic -- CHAPTER 28. The Situation over ℤ: Results -- CHAPTER 29. The Situation over ℤ: Questions -- CHAPTER 30. Appendix: Deligne's Fibre Functor -- Bibliography -- Index
Record Nr. UNINA-9910789730903321
Katz Nicholas M. <1943->  
Princeton ; ; Oxford, : Princeton University Press, c2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Convolution and equidistribution : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
Convolution and equidistribution : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
Autore Katz Nicholas M. <1943->
Edizione [Course Book]
Pubbl/distr/stampa Princeton ; ; Oxford, : Princeton University Press, c2012
Descrizione fisica 1 online resource (213 p.)
Disciplina 515/.723
Collana Annals of mathematics studies
Soggetto topico Mellin transform
Convolutions (Mathematics)
Sequences (Mathematics)
Soggetto non controllato ArtinГchreier reduced polynomial
Emanuel Kowalski
EulerАoincar formula
Frobenius conjugacy class
Frobenius conjugacy
Frobenius tori
GoursatЋolchinВibet theorem
Kloosterman sheaf
Laurent polynomial
Legendre
Mellin transform
Pierre Deligne
Ron Evans
Tannakian category
Tannakian groups
Zeeev Rudnick
algebro-geometric
autodual objects
autoduality
characteristic two
connectedness
dimensional objects
duality
equidistribution
exponential sums
fiber functor
finite field Mellin transform
finite field
finite fields
geometrical irreducibility
group scheme
hypergeometric sheaf
interger monic polynomials
isogenies
lie-irreducibility
lisse
middle convolution
middle extension sheaf
monic polynomial
monodromy groups
noetherian connected scheme
nonsplit form
nontrivial additive character
number theory
odd characteristic
odd prime
orthogonal case
perverse sheaves
polynomials
pure weight
semisimple object
semisimple
sheaves
signs
split form
supermorse
theorem
theorems
ISBN 1-283-37996-1
9786613379962
1-4008-4270-0
Classificazione SI 830
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front matter -- Contents -- Introduction -- CHAPTER 1. Overview -- CHAPTER 2. Convolution of Perverse Sheaves -- CHAPTER 3. Fibre Functors -- CHAPTER 4. The Situation over a Finite Field -- CHAPTER 5. Frobenius Conjugacy Classes -- CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith -- CHAPTER 7. The Main Theorem -- CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility -- CHAPTER 9. Autodualities and Signs -- CHAPTER 10. A First Construction of Autodual Objects -- CHAPTER 11. A Second Construction of Autodual Objects -- CHAPTER 12. The Previous Construction in the Nonsplit Case -- CHAPTER 13. Results of Goursat-Kolchin-Ribet Type -- CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick -- CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family -- CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith -- CHAPTER 17. GL(n) Examples -- CHAPTER 18. Symplectic Examples -- CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples -- CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples -- CHAPTER 21. SL(n) Examples, for n an Odd Prime -- CHAPTER 22. SL(n) Examples with Slightly Composite n -- CHAPTER 23. Other SL(n) Examples -- CHAPTER 24. An O(2n) Example -- CHAPTER 25. G2 Examples: the Overall Strategy -- CHAPTER 26. G2 Examples: Construction in Characteristic Two -- CHAPTER 27. G2 Examples: Construction in Odd Characteristic -- CHAPTER 28. The Situation over ℤ: Results -- CHAPTER 29. The Situation over ℤ: Questions -- CHAPTER 30. Appendix: Deligne's Fibre Functor -- Bibliography -- Index
Record Nr. UNINA-9910824873803321
Katz Nicholas M. <1943->  
Princeton ; ; Oxford, : Princeton University Press, c2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui