Tetragonal modular curves
نویسندگان
چکیده
منابع مشابه
Modular Curves
H is the upper half plane, a complex manifold. It will be helpful to interpret H in multiple ways. A lattice Λ ⊂ C is a free abelian group of rank 2, for which the map Λ ⊗Z R → C is an isomorphism. In other words, Λ is a subgroup of C of the form Zα⊕Zβ, where {α, β} is basis for C/R. Two lattices Λ and Λ′ are homothetic if Λ′ = θΛ for some θ ∈ C∗. This is an equivalence relation, and the equiva...
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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 fu...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2005
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa120-3-6