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Article Dans Une Revue Journal of Geometry and Physics Année : 2019

Efficient computation of multidimensional theta functions

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Résumé

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
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Dates et versions

hal-02173551 , version 1 (22-10-2021)

Licence

Paternité - Pas d'utilisation commerciale - CC BY 4.0

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Jörg Frauendiener, Carine Jaber, Christian Klein. Efficient computation of multidimensional theta functions. Journal of Geometry and Physics, 2019, 141, pp.147-158. ⟨10.1016/j.geomphys.2019.03.011⟩. ⟨hal-02173551⟩
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