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.
Do you ask about solution to high degree polynomials?The following are some reference:
Mumford,Tate lecture II ,appendix(Umemura) 1984.
Bers, Bulletin of London Math. Soc. 4(1972) 257-300;
Klein, Lectures on the icosahedron, 2nd edition,Dover, 1956;
Prasolov and Solovyev, Elliptic functions and elliptic integrals, Amer. Math. Soc. 1997.
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