Explicit computation of the Abel-Jacobi map and its inverse. (Calcul explicite de l'application d'Abel-Jacobi et son inverse)

@inproceedings{Labrande2016ExplicitCO,
  title={Explicit computation of the Abel-Jacobi map and its inverse. (Calcul explicite de l'application d'Abel-Jacobi et son inverse)},
  author={Hugo Labrande},
  year={2016}
}
The Abel-Jacobi map links the short Weierstrass form of a complex elliptic curve to the complex torus associated to it. One can compute it with a number of operations which is quasi-linear in the target precision, i.e. in time O(M(P) log P). Its inverse is given by Weierstrass's p-function, which can be written as a function of theta, an important function in number theory. The natural algorithm for evaluating theta requires O(M(P) sqrt(P)) operations, but some values (the theta-constants) can… Expand
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