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International audienceWe outline an algorithm to compute θ(z, τ) in genus 2 in quasi-optimal time, borrowing ideas from the algorithm for theta constants and the one for θ(z, τ) 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

Computing theta functions in quasi-linear time in genus two and above