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# Generators and equations for modular function fields of principal congruence subgroups

@inproceedings{Ishida1998GeneratorsAE, title={Generators and equations for modular function fields of principal congruence subgroups}, author={Nobuhiko Ishida}, year={1998} }

- Published 1998
DOI:10.4064/aa-85-3-197-207

C(X(N)) = C(s, t), FN (s, t) = 0, FN (X,Y ) ∈ Z[ζN ][X,Y ], where FN (X,Y ) is a polynomial of two variablesX and Y such that FN (s, Y ) = 0 is an irreducible equation of t over kN (s). Note that C(X(N)) can be identified with the field A(N) of all the modular functions with respect to Γ (N). Further, the function field kN (X(N)) of X(N) rational over kN is identified with the field FN of all the modular functions of A(N) with kN -rational Fourier coefficients at the cusp i∞. (See §6.2 of… CONTINUE READING

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