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. 
@article{IM2_2023_87_6_a3,
     author = {A. A. Illarionov},
     title = {Calculation of hyperelliptic systems of sequences of rank 4},
     journal = {Izvestiya. Mathematics },
     pages = {1185--1209},
     publisher = {mathdoc},
     volume = {87},
     number = {6},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a3/}
}
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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/