Geodesic
Calculation of hyperelliptic systems of sequences of rank 4
Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1185-1209.

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Formulas for sequences of complex numbers satisfying functional relations of bilinear type are investigated. The results obtained are used in describing all 1-periodic entire functions $f,g\colon \mathbb{C}\to\mathbb{C}$ satisfying $f(x+y)g(x-y)=\phi_1(x)\psi_1(y)+\dots+\phi_4(x)\psi_4(y)$ for some $\phi_j,\psi_j\colon \mathbb{C}\to\mathbb{C}$.
Keywords: addition theorems, elliptic functions, functional equations, nonlinear recurrent sequences. 
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A. A. Illarionov. Calculation of hyperelliptic systems of sequences of rank 4. Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1185-1209. http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a3/

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