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Graduate Student Number Theory Learning Seminar

A Theorem on the Base Eigenvalues of Hecke Groups

Alex Karlovitz

Location:  This semester talks on Wednesdays, 9:20-10:20 via google hangouts using the Link below
Date & time: Wednesday, 01 April 2020 at 9:20AM - 10:20AM

Given a Fuchsian group Gamma, there is a fascinating relationship (due to Patterson-Sullivan) between the Hausdorff dimension of Gamma's limit set and the smallest eigenvalue of the Laplacian acting on automorphic functions on Gamma\H. In this talk, I will state this relationship as well some results known about these two values. Then, I will explain a theorem of Philips-Sarnak regarding the base eigenvalue in the case where Gamma is a Hecke group.

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