This question The radical solution of a solvable 17th degree equation
and these wikipedia pages:
https://en.wikipedia.org/wiki/Plastic_number#Number_theory
https://en.wikipedia.org/wiki/Bring_radical#Other_characterizations
use the Dedekind eta function to express roots of a polynomial. Is there a theorem or a (specific) field of mathematics where one can learn how to express roots in terms of Dedekind eta functions and which roots are expressible in this manner ?