@KConrad That's actually very close to what I'm studying. Thank you!

@JoeSilverman Those are all terms I know, just not in the context they are in in that linked paper. Your suggestions are incredibly helpful, though. Do you think Neukirch may be the way to go for those? I already have a book on modular forms and curves ("Elliptic curves, modular forms and their L-Functions")

@Bombyx mori I’m currently researching in a seemingly completely unrelated field (a family of functions encoding the eigenvalues of the Laplacian of a compact Riemannian manifold), and I started seeing this formula pop up in the literature. I’m really motivated to understand the weird connection there; and it’s not a school project so ive got plenty of time.

@Bombyxmori Not much at all.