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arXiv · 2603.23188

Computation of genus 2 Kleinian hyperelliptic functions via Richelot isogenies

Matvey Smirnov
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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.

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Matvey Smirnov. 2026-03-24. Computation of genus 2 Kleinian hyperelliptic functions via Richelot isogenies. https://arxiv.org/abs/2603.23188

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