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.
Series: Annals of mathematics studies ; no. 176.c2011Description: 1 online resource (xi, 425 p.) : illSubject(s): Genre/Form: Additional physical formats: Print version:: Computational aspects of modular forms and Galois representations.Online resources:
eBooks
Description based on print version record.
"Edited by Bas Edixhoven and Jean-Marc Couveignes with Robin de Jong, Franz Merkl and Johan Bosman"--Cover.
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 X(esc)b1(esc)s(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.
Includes bibliographical references (p. [403]-421) and index.