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Sign choices in the AGM for genus two theta constants

Jean Kieffer 1, 2
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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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Submitted on : Wednesday, October 14, 2020 - 5:33:33 PM
Last modification on : Saturday, December 4, 2021 - 3:44:00 AM


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  • HAL Id : hal-02967220, version 1
  • ARXIV : 2010.07579



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



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