Sign choices in the AGM for genus two theta constants
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.
Domains
Number Theory [math.NT]
Origin : Files produced by the author(s)
Loading...