Computation of genus 2 Kleinian hyperelliptic functions via Richelot isogenies
Complex Variables
2026-03-25 v1
Abstract
In this work we propose an algorithm that numerically evaluates Kleinian hyperelliptic functions associated with a complex curve of genus 2. This algorithm is based upon constructing a sequence of curves with Richelot isogenous Jacobians and a recurrent procedures that reduces the calculation to a degenerate curve. As a part of mentioned algorithm we propose a method of choosing a Richelot isogenous curve (among 15 possibilities) that guarantees convergence of the equations of the curves and associated Kleinian functions of weight 2 under iterations.
Keywords
Cite
@article{arxiv.2603.23188,
title = {Computation of genus 2 Kleinian hyperelliptic functions via Richelot isogenies},
author = {Matvey Smirnov},
journal= {arXiv preprint arXiv:2603.23188},
year = {2026}
}