论文标题
雅各比反转问题的解决方案
Solution of the Jacobi inversion problem on non-hyperelliptic curves
论文作者
论文摘要
在本文中，我们提出了一种解决雅各比反转问题的方法，该问题是乘以周期性$ \ wp $函数，也称为kleinian $ \ wp $函数。该结果基于$（n，s）$曲线的最近开发的多变量Sigma函数理论。考虑到$（n，s）$ - 曲线是在双理性等效平面代数曲线的相应类别中的规范代表，我们声称平面代数曲线上的jacobi反转问题得到了完全解决。在三角形，四方和五边形曲线上的明确解作为例证。
In this paper we propose a method of solving the Jacobi inversion problem in terms of multiply periodic $\wp$ functions, also called Kleinian $\wp$ functions. This result is based on the recently developed theory of multivariable sigma functions for $(n,s)$-curves. Considering $(n,s)$-curves as canonical representatives in the corresponding classes of bi-rationally equivalent plane algebraic curves, we claim that the Jacobi inversion problem on plane algebraic curves is solved completely. Explicit solutions on trigonal, tetragonal and pentagonal curves are given as an illustration.
