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Automorphism groups of the modular curves \(X_ 0(N)\). (English) Zbl 0686.14035
The authors determine the automorphism group of the modular curve \(X_ 0(N)\) for which the genus \(g_ 0(N)\geq 2\) and for which \(N\neq 37, 63\). They prove that \(Aut(X_ 0(N))=\Gamma^*_ 0(N)/\Gamma_ 0(N)\) with \(\Gamma^*_ 0(N)\) the normalization of \(\Gamma_ 0(N)/\pm 1\) in \(PGL^+(2,{\mathbb{Q}})\). The group \(Aut(X_ 0(37))\) is known, but the case \(N=63\) is still open.
Reviewer: G.van der Geer

MSC:
14H25 Arithmetic ground fields for curves
11F03 Modular and automorphic functions
14L30 Group actions on varieties or schemes (quotients)
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