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Journal Articles LMS Journal of Computation and Mathematics Year : 2016

Computing theta functions in quasi-linear time in genus 2 and above

Abstract

We 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.
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Dates and versions

hal-01277169 , version 1 (22-02-2016)

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Hugo Labrande, Emmanuel Thomé. Computing theta functions in quasi-linear time in genus 2 and above. LMS Journal of Computation and Mathematics, 2016, Special issue: Algorithmic Number Theory Symposium XII, 19 (A), pp.163-177. ⟨10.1112/S1461157016000309⟩. ⟨hal-01277169⟩
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