Journal of Mathematical Sciences

, Volume 243, Issue 6, pp 872–879

# On Products of Weierstrass Sigma Functions

Article
We prove the following result. Let f : ℂ ℂ be an even entire function. Assume that there exist 𝛼j, βj : 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.

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