Geodesic
Hyperelliptic system of sequences and functions
Dalʹnevostočnyj matematičeskij žurnal, Tome 16 (2016) no. 2, pp. 115-122 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article offers a new method for constructing the pairs of functions which are holomorphic on the whole complex plane and satisfy functional equations such as the addition theorem for theta functions. 
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M. O. Avdeeva; V. A. Bykovskii. Hyperelliptic system of sequences and functions. Dalʹnevostočnyj matematičeskij žurnal, Tome 16 (2016) no. 2, pp. 115-122. http://geodesic.mathdoc.fr/item/DVMG_2016_16_2_a0/

[1] K. F. Gauss, “Zur Theorie der neuen Transscendenten”, Werke: Dritter Band [III], Königlichen Gesellschaft der Wissenschaften, Göttingen, 1866 | MR

[2] C. G. J. Jacobi, Gesammelte Werke, v. 1, Berlin, 1881

[3] V. Bykovskii, 2015 http://www.skoltech.ru/app/data/uploads/sites/29/2015/02/Skolkovo_Bykovskii.pdf

[4] R. Rochberg, L. A. Rubel, Indiana Univ. Math. J., 41 (1992), 363–376 | DOI | MR | Zbl