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A geometric Euler totient function associated to non-uniform lattices in SL(2,R)

Samantha Fairchild, University of Washington
Tuesday, May 12, 2020 - 11:00am to 11:50am

We define a generalization of the Euler totient function associated to \Gamma, a subgroup of SL(2,\R) which is discrete, and whose quotient is non-compact but finite volume. When \Gamma = SL(2,Z) the generalization reduces to the classical Euler totient function. We will first discuss a counting result from the study of translation surfaces where the function arises. Next I will share an application of the counting result to understand a generalization of the Gauss circle problem, and propose further questions about the geometric Euler totient function.

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