Equivalent trace sets for arithmetic Fuchsian groups

Lakeland, Grant

doi:10.1090/proc/13194

Equivalent trace sets for arithmetic Fuchsian groups
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Proc. Amer. Math. Soc. 145 (2017), 445-459 Request permission

Abstract:

We show that the modular group has an infinite family of finite index subgroups, each of which has the same trace set as the modular group itself. Various congruence subgroups of the modular group, and the Bianchi groups, are also shown to have this property. In the case of the modular group, we construct examples of such finite index subgroups.

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