Computational Aspects of Modular Forms and Galois Representations : How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176) /

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"This book represents a major step forward from explicit class field theory, and it could be described as the start of the 'explicit Langlands program'"--

Detalles Bibliográficos
Otros Autores: Edixhoven, B. (Bas), 1962-, Couveignes, Jean-Marc
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton : Princeton University Press, 2011.
Colección:Book collections on Project MUSE.
Temas:
Galois modules (Algebra)
Class field theory.
MATHEMATICS > Number Theory.
MATHEMATICS > Algebra > Intermediate.
MATHEMATICS > Geometry > Algebraic.
MATHEMATICS > Advanced.
Theorie du corps de classes.
Modules galoisiens.
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Introduction, main results, context / Bas Edixhoven
  • Modular curves, modular forms, lattices, Galois representations / Bas Edixhoven
  • First description of the algorithms / Jean-Marc Couveignes and Bas Edixhoven
  • Short introduction to heights and Arakelov theory / Bas Edixhoven and Robin de Jong
  • Computing complex zeros of polynomials and power series / Jean-Marc Couveignes
  • Computations with modular forms and Galois representations / Johan Bosman
  • Polynomials for projective representations of level one forms / Johan Bosman
  • Description of X₁(5l) / Bas Edixhoven
  • Applying Arakelov theory / Bas Edixhoven and Robin de Jong
  • An upper bound for Green functions on Riemann surfaces / Franz Merkl
  • Bounds for Arakelov invariants of modular curves / Bas Edixhoven and Robin de Jong
  • Approximating V[subscript f] over the complex numbers / Jean-Marc Couveignes
  • Computing V[subscript f] modulo p / Jean-Marc Couveignes
  • Computing the residual Galois representations / Bas Edixhoven
  • Computing coefficients of modular forms / Bas Edixhoven.

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