InforLorV4, Main, Exploration, bibRecord, 000064

Computing theta functions in quasi-linear time in genus 2 and above

Identifieur interne : 000064 ( Main/Exploration ); précédent : 000063; suivant : 000065

Computing theta functions in quasi-linear time in genus 2 and above

Auteurs : Hugo Labrande [France] ; Emmanuel Thomé [France]

Source :

RBID : Hal:hal-01277169

English descriptors

mix :
- Borchardt mean, Quasi-linear time complexity, Theta Functions, Number Theory.

Abstract

We outline an algorithm to compute θ(z, τ) in genus 2 in quasi-optimal time, borrowing ideas from the algorithm for theta constants and the one for θ(z, τ) in genus 1. Our implementation shows a large speedup for precisions as low as a few thousand decimal digits. We also lay out a strategy to generalize this algorithm to genus g.

Url:

https://hal.inria.fr/hal-01277169

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 001799
to stream Hal, to step Curation: 001799
to stream Hal, to step Checkpoint: 000065
to stream Main, to step Merge: 000064
to stream Main, to step Curation: 000064

Le document en format XML

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<front><div type="abstract" xml:lang="en">We outline an algorithm to compute θ(z, τ) in genus 2 in quasi-optimal time, borrowing ideas from the algorithm for theta constants and the one for θ(z, τ) in genus 1. Our implementation shows a large speedup for precisions as low as a few thousand decimal digits. We also lay out a strategy to generalize this algorithm to genus g.</div>
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<region><li>Grand Est</li>
<li>Lorraine (région)</li>
</region>
<settlement><li>Metz</li>
<li>Nancy</li>
</settlement>
<orgName><li>Université de Lorraine</li>
</orgName>
</list>
<tree><country name="France"><region name="Grand Est"><name sortKey="Labrande, Hugo" sort="Labrande, Hugo" uniqKey="Labrande H" first="Hugo" last="Labrande">Hugo Labrande</name>
</region>
<name sortKey="Thome, Emmanuel" sort="Thome, Emmanuel" uniqKey="Thome E" first="Emmanuel" last="Thomé">Emmanuel Thomé</name>
</country>
</tree>
</affiliations>
</record>

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Computing theta functions in quasi-linear time in genus 2 and above

Computing theta functions in quasi-linear time in genus 2 and above

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