Saved in:
Bibliographic Details
Main Authors: Smirnov, Matvey, Malkov, Kirill, Rogovoy, Sergey
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2408.05252
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866909284295507968
author Smirnov, Matvey
Malkov, Kirill
Rogovoy, Sergey
author_facet Smirnov, Matvey
Malkov, Kirill
Rogovoy, Sergey
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2408_05252
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Landen-type method for computation of Weierstrass functions
Smirnov, Matvey
Malkov, Kirill
Rogovoy, Sergey
Complex Variables
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.
title A Landen-type method for computation of Weierstrass functions
topic Complex Variables
url https://arxiv.org/abs/2408.05252