Pré-Publication, Document De Travail Année : 2020

Sign choices in the AGM for genus two theta constants

Résumé

Existing algorithms to compute genus 2 theta constants in quasi-linear time use Borchardt sequences, an analogue of the arithmetic-geometric mean for four complex numbers. In this paper, we show that these Borchardt sequences are given by good choices of square roots only, as in the genus 1 case. This removes the sign indeterminacies in the algorithm without relying on numerical integration.
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Dates et versions

hal-02967220 , version 1 (14-10-2020)
hal-02967220 , version 2 (09-10-2022)

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Jean Kieffer. Sign choices in the AGM for genus two theta constants. 2020. ⟨hal-02967220v1⟩
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