The Theory Of Auxiliary Weierstrassian Zeta Functions And Zeta Differences

2025/04/17 by Efe Gürel, Gürel, Efe
Mathematics · Physics and Astronomy · #33E05 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.12697

openalex publication_date 2025/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• On the universal p-adic sigma and Weierstrass zeta functions
• On functions of Jacobi and Weierstrass (I)
• A new construction of Eisenstein's completion of the Weierstrass zeta function
• A Recipe For Obtaining Algebraic Addition Theorems Of The Weierstrass Elliptic Function
• Koshliakov zeta functions I: Modular Relations