{"title":"A Landen-type method for computation of Weierstrass functions","authors":"Matvey Smirnov, Kirill Malkov, Sergey Rogovoy","doi":"arxiv-2408.05252","DOIUrl":null,"url":null,"abstract":"We establish a version of the Landen's transformation for Weierstrass\nfunctions and invariants that is applicable to general lattices in complex\nplane. Using it we present an effective method for computing Weierstrass\nfunctions, their periods, and elliptic integral in Weierstrass form given\nWeierstrass invariants $g_2$ and $g_3$ of an elliptic curve. Similarly to the\nclassical Landen's method our algorithm has quadratic rate of convergence.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.05252","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We establish a version of the Landen's transformation for Weierstrass
functions and invariants that is applicable to general lattices in complex
plane. Using it we present an effective method for computing Weierstrass
functions, their periods, and elliptic integral in Weierstrass form given
Weierstrass invariants $g_2$ and $g_3$ of an elliptic curve. Similarly to the
classical Landen's method our algorithm has quadratic rate of convergence.
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