Sign choices in the AGM for genus two theta constants
Number Theory
2022-10-11 v2
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.
Keywords
Cite
@article{arxiv.2010.07579,
title = {Sign choices in the AGM for genus two theta constants},
author = {Jean Kieffer},
journal= {arXiv preprint arXiv:2010.07579},
year = {2022}
}