Far Eastern Mathematical Journal

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Hyperelliptic system of sequences and functions


Avdeeva M.O., Bykovskii V.A.

2016, issue 2, Đ. 115-122


Abstract
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

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

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References

[1] K.F. Gauss, źZur 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, źElliptic 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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