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arXiv · 2010.07579

Sign choices in the AGM for genus two theta constants

Jean Kieffer
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Abstract

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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Jean Kieffer. 2020-10-15. Sign choices in the AGM for genus two theta constants. https://doi.org/10.5802/pmb.45

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