Far Eastern Mathematical Journal

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Hyperelliptic system of sequences and functions

Avdeeva M.O., Bykovskii V.A.

2016, issue 2, P.

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

functional equations, theta functions, Weierstrass sigma-function, nonlinear sequences

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[1] K.F. Gauss, «Zur Theorie der neuen Transscendenten», Werke: Dritter Band [III], Koniglichen Gesellschaft der Wissenschaften, Gottingen, 1866.
[2] C. G. J. Jacobi, Gesammelte Werke. V. 1, Berlin, 1881.
[3] V. Bykovskii, «Elliptic systems of sequences and functions», 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.

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