The Atkin-Lehner-Li group of Shimura's modular curve

Abstract: Let X_\chi(N) be the double covering of X_0(N) associated to \chi. We show that the group W_\chi$ generated by the Atkin-Lehner-Li automorphisms w_Q of X_\chi(N) is a central extension of an elementary abelian 2-group. We also characterise when w_Q lies in the centre Z(W_\chi) of W_\chi in terms of genus theory. Finally, we decompose W_\chi as a product of an elementary abelian 2-group with either an extra-special 2-group, the Pauli group, or C_4, if the extension is non-trivial.

algebraic geometrynumber theory

Audience: researchers in the topic

FGC-HRI-IPM Number Theory Webinars

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