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Equivalent trace sets for arithmetic Fuchsian groups


Author: Grant S. Lakeland
Journal: Proc. Amer. Math. Soc. 145 (2017), 445-459
MSC (2010): Primary 57M50; Secondary 20F65
DOI: https://doi.org/10.1090/proc/13194
Published electronically: July 6, 2016
MathSciNet review: 3565394
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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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Grant S. Lakeland
Affiliation: Department of Mathematics and Computer Science, Eastern Illinois University, 600 Lincoln Avenue, Charleston, Illinois 61920
Email: gslakeland@eiu.edu

DOI: https://doi.org/10.1090/proc/13194
Received by editor(s): January 11, 2016
Received by editor(s) in revised form: March 12, 2016
Published electronically: July 6, 2016
Communicated by: David Futer
Article copyright: © Copyright 2016 American Mathematical Society