21.1 Modular Curves
نویسنده
چکیده
Note that Γ(1) = Γ1(1) = Γ0(1) = SL2(Z). We now define the modular curves X(N) = H∗/Γ(N), X1(N) = H/Γ1(N), X0(N) = H/Γ0(N). and similarly define Y (N), Y1(N), and Y0(N), with H∗ replaced by H. Following the same strategy we used for X(1), one can show that these are all compact Riemann surfaces. Having defined the modular curves X(N), X1(N), and X0(N), we now want to consider the meromorphic functions on these curves. We are specifically interested in X0(N), for reasons that will become clear shortly, but we begin with the general setup.
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