Automorphisms of \(X_0^*(p)\). (English) Zbl 1088.11049
Let \(\Gamma_0^*(p)\) denote the normalizer in \(\text{GL}_2^+(\mathbb Q)\) of the Hecke congruence subgroup \(\Gamma_{0}(p)\) of level a prime number \(p\). It is shown that the automorphism group of the modular curve \(X_0^*(p)\) corresponding to the congruence subgroup \(\Gamma_0^*(p)\) is trivial when the genus of the curve \(X_0^*(p)\) is greater than two. It is isomorphic to \(\mathbb Z/2\mathbb Z\) in the case of genus two. Firs they prove the theorem for primes \(p>695\). And the remaining finite set of primes is treated by analyzing the geometry of the curve reduced modulo the prime \(p\).
Reviewer: Olaf Ninnemann (Berlin)
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