The Theory Of Auxiliary Weierstrassian Zeta Functions And Zeta Differences
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909975622713344 |
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| author | Gürel, Efe |
| author_facet | Gürel, Efe |
| contents | In this paper, we expand the theory of Weierstrassian elliptic functions by introducing auxiliary zeta functions $ζ_λ$, zeta differences of first kind $Δ_λ$ and second kind $Δ_{λ,μ}$ where $λ,μ=1,2,3$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Theory Of Auxiliary Weierstrassian Zeta Functions And Zeta Differences Gürel, Efe Complex Variables Number Theory 33E05 In this paper, we expand the theory of Weierstrassian elliptic functions by introducing auxiliary zeta functions $ζ_λ$, zeta differences of first kind $Δ_λ$ and second kind $Δ_{λ,μ}$ where $λ,μ=1,2,3$. 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. |
| title | The Theory Of Auxiliary Weierstrassian Zeta Functions And Zeta Differences |
| topic | Complex Variables Number Theory 33E05 |
| url | https://arxiv.org/abs/2504.12697 |