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Numerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms

hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
dc.contributor.authorJOHANSSON, Fredrik
dc.contributor.editorJohannes Blümlein
dc.contributor.editorCarsten Schneider
dc.contributor.editorPeter Paule
dc.date.accessioned2024-04-04T03:05:42Z
dc.date.available2024-04-04T03:05:42Z
dc.date.issued2019
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193271
dc.description.abstractEnWe describe algorithms to compute elliptic functions and their relatives (Jacobi theta functions, modular forms, elliptic integrals, and the arithmetic-geometric mean) numerically to arbitrary precision with rigorous error bounds for arbitrary complex variables. Implementations in ball arithmetic are available in the open source Arb library. We discuss the algorithms from a concrete implementation point of view, with focus on performance at tens to thousands of digits of precision.
dc.language.isoen
dc.publisherSpringer
dc.source.titleElliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory
dc.title.enNumerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms
dc.typeChapitre d'ouvrage
dc.subject.halInformatique [cs]/Logiciel mathématique [cs.MS]
dc.subject.halInformatique [cs]/Analyse numérique [cs.NA]
dc.identifier.arxiv1806.06725
bordeaux.page269-293
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.title.proceedingElliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory
hal.identifierhal-01817952
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01817952v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Elliptic%20Integrals,%20Elliptic%20Functions%20and%20Modular%20Forms%20in%20Quantum%20Field%20Theory&rft.date=2019&rft.spage=269-293&rft.epage=269-293&rft.au=JOHANSSON,%20Fredrik&rft.genre=unknown


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