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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.23188 |
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| _version_ | 1866918406630932480 |
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| author | Smirnov, Matvey |
| author_facet | Smirnov, Matvey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23188 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computation of genus 2 Kleinian hyperelliptic functions via Richelot isogenies Smirnov, Matvey Complex Variables 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. |
| title | Computation of genus 2 Kleinian hyperelliptic functions via Richelot isogenies |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2603.23188 |