I am currently learning Riemann surfaces and am wondering if learning modular forms would be helpful (like improving my understand, introducing more useful tools in Riemann surfaces,etc), since books in modular forms like the one by Milne has a chapter talking about Riemann surfaces.

Thanks for your advice in advance.

  • 1
    $\begingroup$ Modular curves classify elliptic curves so you can't really avoid them in the theory of Riemann surfaces. Modular forms use a lot of different fields but Riemann surfaces too, they are the arithmetic counterpart ($\zeta(s)$ and L-functions). The problems about the jacobian of $X_0(n)$ and Galois representations and reductions $\mod p$ is a way to start with algebraic geometry and algebraic number theory. $\endgroup$ – reuns Sep 8 at 19:25

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