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.



Quintic polynomial solution by Jacobi Theta function.
Do you ask about solution to high degree polynomials? The following are some reference:


* 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](https://doi.org/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](https://doi.org/10.1112/blms/4.3.257)
* F. Klein, *Lectures on the icosahedron*, 2nd edition, Dover, 1956; [Internet Archive](https://archive.org/details/cu31924059413439)
* Prasolov and Solovyev, *Elliptic functions and elliptic integrals*,
Translations of Mathematical Monographs 1997. [AMS bookstore](https://bookstore.ams.org/mmono-170)
* Richard J. Drociuk, *On the Complete Solution to the Most General Fifth Degree Polynomial* <https://arxiv.org/abs/math/0005026>


