辅助 Weierstrass 齐次函数理论与齐次差分

Efe Gürel

辅助 Weierstrass 齐次函数理论与齐次差分

复变函数 2025-12-29 v3 数论

作者: Efe Gürel

摘要

本文通过引入辅助齐次函数 $\zeta_\lambda$ 、第一类齐次差分 $\Delta_\lambda$ 和第二类齐次差分 $\Delta_{\lambda,\mu}$ （其中 $\lambda,\mu=1,2,3$ ），扩展了 Weierstrass 仿射函数的理论。证明了关于这些函数的基本且新颖的结果。此外，已存在于文献中的结果以辅助齐次函数的形式翻译。它们与 Jacobian 仿射函数和 Jacobian 函数的关系被给出。

关键词

Weierstrass 仿射函数辅助齐次函数齐次差分 Jacobian 仿射函数数学理论

引用

@article{arxiv.2504.12697,
  title  = {The Theory Of Auxiliary Weierstrassian Zeta Functions And Zeta Differences},
  author = {Efe Gürel},
  journal= {arXiv preprint arXiv:2504.12697},
  year   = {2025}
}

备注

This paper was planned to be the first paper of a 4-paper long series on theory of auxiliary zeta functions. These papers, whose first two are already prepared, would provide a whole theory for these new functions.The author has decided that it is better publish his findings in a complete manner in a single paper as it would give a more total and satisfactory view of the newly developed theory

辅助 Weierstrass 齐次函数理论与齐次差分

摘要

关键词

引用

备注

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