计算魏尔斯特拉斯函数的兰登式方法

arXiv - MATH - Complex Variables Pub Date : 2024-08-08 DOI:arxiv-2408.05252

Matvey Smirnov, Kirill Malkov, Sergey Rogovoy

{"title":"计算魏尔斯特拉斯函数的兰登式方法","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":"{\"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}","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

摘要

我们建立了一个适用于复平面一般网格的魏尔斯特拉斯函数和不变式的兰登变换版本。利用它，我们提出了一种有效的方法，在给定椭圆曲线的魏尔斯特拉斯不变式 $g_2$ 和 $g_3$ 的情况下，以魏尔斯特拉斯形式计算魏尔斯特拉斯函数及其周期和椭圆积分。与经典的兰登方法类似，我们的算法具有二次收敛率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A Landen-type method for computation of Weierstrass functions

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Complex Variables

自引率

0.00%

发文量