Browsing by Subject "representation-theory"
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Item The Selberg Trace Formula for Rank One Spaces(2021-12) Chatterjee, Ryan; Bowen, LewisThe goal of this paper is to explain a result due to Selberg used in the spectral theory of hyperbolic surfaces, called the Selberg Trace Formula. This result has a generalization to the representation theory of locally compact topological groups. We cover the original result of Selberg regarding hyperbolic surfaces, then turn our attention to the general theory. In the specific case of a rank one semisimple real Lie group, we provide a rather explicit version of this formula. Finally, we return our attention to SL2(R) to demonstrate how the very abstract version of the trace formula is indeed equivalent to the complicated, explicit expression derived in the first section.