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arXiv · 1509.01490

On degenerate sigma-functions of genus two

Julia Bernatska·Dmitry Leykin
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Abstract

We obtain explicit expressions for genus 2 degenerate sigma-function in terms of genus $1$ sigma-function and elementary functions as solutions of a system of linear PDEs satisfied by the sigma-function. By way of application we derive a solution for a class of generalized Jacobi inversion problems on elliptic curves, a family of Schrödinger-type operators on a line with common spectrum consisting of a point and two segments, explicit construction of a field of three-periodic meromorphic functions. Generators of rank $3$ lattice in $\mathbb{C}^2$ are given explicitly.

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Julia Bernatska, Dmitry Leykin. 2016-10-31. On degenerate sigma-functions of genus two. https://doi.org/10.1017/s0017089518000162

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