Numerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| dc.contributor.author | JOHANSSON, Fredrik | |
| dc.contributor.editor | Johannes Blümlein | |
| dc.contributor.editor | Carsten Schneider | |
| dc.contributor.editor | Peter Paule | |
| dc.date.accessioned | 2024-04-04T03:05:42Z | |
| dc.date.available | 2024-04-04T03:05:42Z | |
| dc.date.issued | 2019 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193271 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.publisher | Springer | |
| dc.source.title | Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory | |
| dc.title.en | Numerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms | |
| dc.type | Chapitre d'ouvrage | |
| dc.subject.hal | Informatique [cs]/Logiciel mathématique [cs.MS] | |
| dc.subject.hal | Informatique [cs]/Analyse numérique [cs.NA] | |
| dc.identifier.arxiv | 1806.06725 | |
| bordeaux.page | 269-293 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.title.proceeding | Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory | |
| hal.identifier | hal-01817952 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01817952v1 | |
| bordeaux.COinS | ctx_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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