双曲函数域中的生成元
Generators in the field of hyperelliptic functions
AI总结：
本文研究了双曲函数域的生成元，证明了其与有理函数域同构，并指出这些生成元之间不存在代数关系。
摘要：
我们考虑了对于一族双曲曲线定义的双曲函数域，作为某些来自克莱因函数理论的特殊函数的有理函数。我们比较了我们的定义与经典定义。我们提供了结果的细节和参考文献，即对于一族双曲曲线 genus 为 g 的双曲函数域，与具有 3g 个生成元的有理函数域同构。本文的主要结果是这些生成元之间没有代数关系。
英文摘要：
We consider the field of hyperelliptic functions defined for a family of hyperelliptic curves as rational functions in some special functions from Kleinian functions theory. We compare our definition with the classical one. We provide details and references for the result that the field of hyperelliptic functions for a family of hyperelliptic curves of genus $g$ is isomorphic to the field of rational functions with $3g$ generators. The main result of the present work is that there are no algebraic relations between these generators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
