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arXiv · 1305.4330

Computing class polynomials for abelian surfaces

Andreas Enge·Emmanuel Thomé
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Abstract

We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 curves via complex floating-point approximations of their roots. After providing an explicit treatment of the computations in quartic CM fields and their Galois closures, we pursue an approach due to Dupont for evaluating $\theta$- constants in quasi-linear time using Newton iterations on the Borchardt mean. We report on experiments with our implementation and present an example with class number 17608.

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Andreas Enge, Emmanuel Thomé. 2013-05-19. Computing class polynomials for abelian surfaces. https://arxiv.org/abs/1305.4330

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