Geodesic
On products of Weierstrass sigma functions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 73-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove the following result. Let $f\colon\mathbb C\to\mathbb C$ be an even entire function. Let there exist $\alpha_j,\beta_j\colon\mathbb C\to\mathbb C$ with $$ f(x+y) f(x-y) = \sum_{j=1}^4\alpha_j(x)\beta_j(y),\qquad x,y\in\mathbb C. $$ Then $f(z)=\sigma_L(z)\cdot\sigma_\Lambda(z)\cdot e^{Az^2+C}$, where $L$ and $\Lambda$ are lattices in $\mathbb C$, $\sigma_L$ is the Weierstrass sigma function associated to the lattice $L$, and $A,C\in\mathbb C$. 
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     title = {On products of {Weierstrass} sigma functions},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a7/}
}
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A. A. Illarionov. On products of Weierstrass sigma functions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 73-84. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a7/

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