Abstract : An important step in the efficient computation of multi-dimensional theta functions is the construction of appropriate symplectic transformations for a given Riemann matrix assuring a rapid convergence of the theta series. An algorithm is presented to approximately map the Riemann matrix to the Siegel fundamental domain. The shortest vector of the lattice generated by the Riemann matrix is identified exactly, and the algorithm ensures that its length is larger than root 3/2. The approach is based on a previous algorithm by Deconinck et al.. using the LLL algorithm for lattice reductions. Here, the LLL algorithm is replaced by exact Minkowski reductions for small genus and an exact identification of the shortest lattice vector for larger values of the genus
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02173551 Contributeur : Accord Elsevier CCSDConnectez-vous pour contacter le contributeur Soumis le : vendredi 22 octobre 2021 - 18:08:37 Dernière modification le : mercredi 3 novembre 2021 - 06:12:47 Archivage à long terme le : : lundi 24 janvier 2022 - 17:00:58