Kleinian Hyperelliptic Functions of Weight 2 Associated with Curves of Genus 2
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).
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Analytic and geometric function theory
Advanced Mathematical Identities
Publication details
- Journal / source
- Lobachevskii Journal of Mathematics
- Publisher
- Pleiades Publishing Ltd
- Volume
- 47
- Issue
- 2
- Pages
- 901–916
- Publication date
- 1 February 2026
- Language
- EN