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Computational aspects of modular forms and Galois representations : how one can compute in polynomial time the value of Ramanujan's tau at a prime /
"Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fas...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
©2011.
|
| Colección: | Annals of mathematics studies ;
no. 176. |
| Temas: | |
| 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.