Computing class polynomials for abelian surfaces
Identifieur interne : 000D71 ( Main/Exploration ); précédent : 000D70; suivant : 000D72Computing class polynomials for abelian surfaces
Auteurs : Andreas Enge [France] ; Emmanuel Thomé [France]Source :
- Experimental Mathematics [ 1058-6458 ] ; 2014.
English descriptors
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:
DOI: 10.1080/10586458.2013.878675
Affiliations:
- France
- Aquitaine, Grand Est, Lorraine (région), Nouvelle-Aquitaine
- Bordeaux, Metz, Nancy
- Université de Bordeaux, Université de Lorraine
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: 001784
- to stream Hal, to step Curation: 001784
- to stream Hal, to step Checkpoint: 000D52
- to stream Main, to step Merge: 000D69
- to stream Main, to step Curation: 000D71
Le document en format XML
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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></front></TEI><affiliations><list><country><li>France</li></country><region><li>Aquitaine</li><li>Grand Est</li><li>Lorraine (région)</li><li>Nouvelle-Aquitaine</li></region><settlement><li>Bordeaux</li><li>Metz</li><li>Nancy</li></settlement><orgName><li>Université de Bordeaux</li><li>Université de Lorraine</li></orgName></list><tree><country name="France"><region name="Nouvelle-Aquitaine"><name sortKey="Enge, Andreas" sort="Enge, Andreas" uniqKey="Enge A" first="Andreas" last="Enge">Andreas Enge</name></region><name sortKey="Thome, Emmanuel" sort="Thome, Emmanuel" uniqKey="Thome E" first="Emmanuel" last="Thomé">Emmanuel Thomé</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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