The Theory Of Auxiliary Weierstrassian Zeta Functions And Zeta Differences

Efe Gürel

The Theory Of Auxiliary Weierstrassian Zeta Functions And Zeta Differences

Complex Variables 2025-12-29 v3 Number Theory

Authors: Efe Gürel

Abstract

In this paper, we expand the theory of Weierstrassian elliptic functions by introducing auxiliary zeta functions $\zeta_\lambda$ , zeta differences of first kind $\Delta_\lambda$ and second kind $\Delta_{\lambda,\mu}$ where $\lambda,\mu=1,2,3$ . Fundamental and novel results pertaining to these functions are proven. Furthermore, results already existing in the literature are translated in terms of auxiliary zeta functions. Their relationship to Jacobian elliptic functions and Jacobian functions are given.

Keywords

Weierstrassian elliptic functions auxiliary zeta functions zeta differences Jacobian elliptic functions mathematical theory

Cite

@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}
}

Comments

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

The Theory Of Auxiliary Weierstrassian Zeta Functions And Zeta Differences

Abstract

Keywords

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