Geodesic
Hyperelliptic systems of sequences of rank~4
Sbornik. Mathematics, Tome 210 (2019) no. 9, pp. 1259-1287

Voir la notice de l'article provenant de la source Math-Net.Ru

Sequences of complex numbers satisfying functional relations of bilinear type are investigated. The results obtained are used in describing all 1-periodic entire functions $f\colon \mathbb C\to\mathbb C$ such that the expansion ${f(x+y)f(x-y)}=\varphi_1(x)\psi_1(y)+\dots+\varphi_4(x)\psi_4(y)$ holds for some $\varphi_j,\psi_j\colon\mathbb C\to\mathbb C$. Bibliography: 38 titles.
Keywords: addition theorems, elliptic functions, functional equations, nonlinear recurrent sequences. 
@article{SM_2019_210_9_a2,
     author = {A. A. Illarionov},
     title = {Hyperelliptic systems of sequences of rank~4},
     journal = {Sbornik. Mathematics},
     pages = {1259--1287},
     publisher = {mathdoc},
     volume = {210},
     number = {9},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_9_a2/}
}
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A. A. Illarionov. Hyperelliptic systems of sequences of rank~4. Sbornik. Mathematics, Tome 210 (2019) no. 9, pp. 1259-1287. http://geodesic.mathdoc.fr/item/SM_2019_210_9_a2/