Computing class polynomials for abelian surfaces
ENGE, Andreas
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
ENGE, Andreas
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
Experimental Mathematics. 2014, vol. 23, n° 2, p. 129-145
Taylor & Francis
English 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 ...Read more >
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 ϑ- 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 20016.Read less <
English Keywords
Number theory
Complex Multiplication
Theta functions
European Project
Algorithmic Number Theory in Computer Science
Origin
Hal imported