Kleinian hyperelliptic funtions of weight 2 associated with curves of genus 2
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912955217477632 |
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| author | Smirnov, Matvey |
| author_facet | Smirnov, Matvey |
| contents | We introduce a new collection of special functions associated to a complex curve of genus 2 similar to Kleinian hyperelliptic $σ$-function. These functions are related to weight 2 $θ$-functions in the same fashion as $σ$-function is related to the classical $θ$-function. A key feature of the introduced functions is the fact that they are well-defined for genus 2 algebraic curves without any restrictions (in particular it is not needed to assume that the curve has a Weierstrass point at infinity). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08253 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kleinian hyperelliptic funtions of weight 2 associated with curves of genus 2 Smirnov, Matvey Complex Variables We introduce a new collection of special functions associated to a complex curve of genus 2 similar to Kleinian hyperelliptic $σ$-function. These functions are related to weight 2 $θ$-functions in the same fashion as $σ$-function is related to the classical $θ$-function. A key feature of the introduced functions is the fact that they are well-defined for genus 2 algebraic curves without any restrictions (in particular it is not needed to assume that the curve has a Weierstrass point at infinity). |
| title | Kleinian hyperelliptic funtions of weight 2 associated with curves of genus 2 |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2603.08253 |