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arXiv · 2603.08253

Kleinian hyperelliptic funtions of weight 2 associated with curves of genus 2

Matvey Smirnov
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Abstract

We introduce a new collection of special functions associated to a complex curve of genus 2 similar to Kleinian hyperelliptic $\sigma$-function. These functions are related to weight 2 $\theta$-functions in the same fashion as $\sigma$-function is related to the classical $\theta$-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).

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Matvey Smirnov. 2026-03-09. Kleinian hyperelliptic funtions of weight 2 associated with curves of genus 2. https://arxiv.org/abs/2603.08253

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