On Products of Weierstrass Sigma Functions
- Authors: Illarionov A.A.1
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Affiliations:
- Khabarovsk Division of the Institute for Applied Mathematics and Pacific National University
- Issue: Vol 243, No 6 (2019)
- Pages: 872-879
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/243176
- DOI: https://doi.org/10.1007/s10958-019-04587-1
- ID: 243176
Cite item
Abstract
We prove the following result. Let f : ℂ → ℂ be an even entire function. Assume that there exist ????j, βj : ℂ → ℂ with
\( f\left(x+y\right)f\left(x-y\right)=\sum \limits_{\mathrm{j}=1}^4{\alpha}_j(x){\beta}_j(y),\kern0.5em x,y\in \mathbb{C}. \)
Then f(z) = σL(z) · σΛ(z) · eAz2+C where L and Λ are lattices in ℂ, σL is the Weierstrass sigma function associated with the lattice L, and A,C ∈ ℂ.
About the authors
A. A. Illarionov
Khabarovsk Division of the Institute for Applied Mathematics and Pacific National University
Author for correspondence.
Email: illar_a@list.ru
Russian Federation, Khabarovsk