InforLorV4, Hal, Checkpoint, bibRecord, 000D52

Computing class polynomials for abelian surfaces

Identifieur interne : 000D52 ( Hal/Checkpoint ); précédent : 000D51; suivant : 000D53

Computing class polynomials for abelian surfaces

Auteurs : Andreas Enge [France] ; Emmanuel Thomé [France]

Source :

Experimental Mathematics [ 1058-6458 ] ; 2014.

RBID : Hal:hal-00823745

English descriptors

mix :
- Complex Multiplication, Number theory, Theta functions.

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 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.

Url:

https://hal.inria.fr/hal-00823745

DOI: 10.1080/10586458.2013.878675

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Le document en format XML

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<front><div type="abstract" xml:lang="en">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.</div>
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<sourceDesc><biblStruct><analytic><title xml:lang="en">Computing class polynomials for abelian surfaces</title>
<author role="aut"><persName><forename type="first">Andreas</forename>
<surname>Enge</surname>
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<author role="aut"><persName><forename type="first">Emmanuel</forename>
<surname>Thomé</surname>
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<idno type="issn">1058-6458</idno>
<title level="j">Experimental Mathematics</title>
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<biblScope unit="pp">129-145</biblScope>
<date type="datePub">2014</date>
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<idno type="arxiv">1305.4330</idno>
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<textClass><keywords scheme="author"><term xml:lang="en">Number theory</term>
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<abstract xml:lang="en">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.</abstract>
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Computing class polynomials for abelian surfaces

Computing class polynomials for abelian surfaces

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