Sign choices in the AGM for genus two theta constants
Jean Claude Kieffer · Publications mathématiques de Besançon · 2022
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 only given by good choices of square roots, as in the genus 1 case. This removes the sign indeterminacies when computing genus 2 theta constants without relying on numerical integration.