International Association
for Cryptologic Research

We outline an algorithm to compute $\theta(z,\tau)$ in genus 2 in quasi-optimal time, borrowing ideas from the algorithm for theta constants and the one for $\theta(z,\tau)$ in genus 1. Our implementation shows a large speedup for precisions as low as a few thousand decimal digits. We also lay out a strategy to generalize this algorithm to genus $g$.