Generators and defining equation of the modular function field of the group~\({\varGamma}_1(N)\) (Q2773337)
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scientific article; zbMATH DE number 1709928
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generators and defining equation of the modular function field of the group~\({\varGamma}_1(N)\) |
scientific article; zbMATH DE number 1709928 |
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21 February 2002
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modular curve
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algebraic function field
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generators
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Generators and defining equation of the modular function field of the group~\({\varGamma}_1(N)\) (English)
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For any integer \(N\geq 10\), let \(X_1(N)\) be the modular curve corresponding to the group \(\Gamma_1(N)\leq \text{SL}_2(\mathbb{Z})\) and \(K_1(N)\) be the algebraic function field corresponding to \(X_1(N)\). The authors construct generators of \(K_1(N)\) over \(\mathbb{C}\) which satisfy easy equations. The construction follows ideas of Lecacheux, Washington and Darmon.
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