Efficient computation of multidimensional theta functions

Understand

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 $\sqrt{3}/2$.
• The approach is based on a previous algorithm by Deconinck et al.