I was looking at the Davidson $2021$ fellows and decided to take a look at Apoorva's paper. What fields of math do I need to learn to understand her research paper? Currently I know most of Complex Analysis but that is it. I am thinking the paper is using algebraic number theory because of the use of sets and elliptic curves.
2026-03-26 19:17:23.1774552643
Fields of math to learn to understand this paper
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From the abstract, here are some keywords
Elliptic curves you can learn about from Silverman's book(s) and other places. Quadratic fields would be talked about in algebraic number theory or Galois theoroy (field extension by a square root). Holomorphic and Fourier stuff is complex analysis and Fourier analysis although when they say "coefficients" that just means "write this function as a sum $\sum_{n \in \mathbf{Z}} a_n e^{2\pi i n}$" and you don't need too much Fourier analysis to understand that part.
Complex multiplication and "newforms" would be covered in a book on modular forms which is something you haven't mentioned. I'm not super familiar with modular forms but I believe Koblitz's book "Elliptic curves and modular forms" is a good introduction.