Geodesic
On the connection between hyperelliptic systems of sequences and functions
Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 2, pp. 210-220.

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We study the connection between $1$-periodic solutions of the functional equation $$ f(x+y)g(x-y)=\sum_{j=1}^N\varphi_j(x)\psi_j(y) \quad (x,y\in \mathbb C) $$ and some sequences of special kind. As an application we solve the equation in the case when $g$ is Jacobi theta function. 
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A. A. Illarionov; M. A. Romanov. On the connection between hyperelliptic systems of sequences and functions. Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 2, pp. 210-220. http://geodesic.mathdoc.fr/item/DVMG_2017_17_2_a8/

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