Riemann theta function [wishlist]

[videlec]

The Riemann theta function is a natural generalization of the Jacobi theta functions. In this more general situation, the invariance involves the integral symplectic group acting on the Siegel half space (there is no nice fundamental domain, though there are some good super sets: the so called "Siegel domains").

An arbitrary precision implementation would be very useful for Riemann surface computations (see e.g. issue 150 in abelfunctions).

[fredrik-johansson]

This would certainly be useful, but I'm not familiar with the algorithms. Are you interested in helping out with an implementation?

[videlec]

Of course!

For future references

• Deconinck et al "Computing Riemann Theta Functions" (2004)
• entry in DLMF
• Deconinck, Swierczewski "Computing Riemann theta functions in Sage with applications" (2016)

[tthsqe12]

I also think this would be useful, but it will be a lot of work.

[fredrik-johansson]

Done in Flint.