Quintic polynomial solution by Jacobi Theta function. Does someone have a good and rigorous reference for the solution of quintic ploynomial equation with Jacobi Theta function, in English?
Mathworld and Wikipedia don't give a good English reference, at least from what I skimmed over.
 A: Do you ask about solution to high degree polynomials? The following are some reference:

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*Umemura H. (2007) Resolution of algebraic equations by theta constants. In: Tata Lectures on Theta II. Modern Birkhäuser Classics. Birkhäuser, Boston, MA. doi:10.1007/978-0-8176-4578-6_18


*L. Bers, Uniformization, Moduli, and Kleinian Groups, Bulletin of London Math. Soc. 4 (1972) 257-300,  doi:10.1112/blms/4.3.257


*F. Klein, Lectures on the icosahedron, 2nd edition, Dover, 1956; Internet Archive


*Prasolov and Solovyev, Elliptic functions and elliptic integrals,
Translations of Mathematical Monographs 1997. AMS bookstore


*Richard J. Drociuk, On the Complete Solution to the Most General Fifth Degree Polynomial https://arxiv.org/abs/math/0005026
A: There's also a very nice, modern exposition by Mark L. Green:  On the analytic solution of the equation of fifth degree, Compositio Mathematica 37 (1978), 233–241.  A pdf of the paper is available online:  http://www.numdam.org/item?id=CM_1978__37_3_233_0
