An explicit integral formula for the heat kernel and the full Laplace spectrum of the Cayley graph of the modular group are derived by solving the spectral problem on a weighted line that the graph covers.
and Karlsson, A., 2015, Heat kernels on regular graphs and generalized Ihara zeta function formulas, Monatsh
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On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$
An explicit integral formula for the heat kernel and the full Laplace spectrum of the Cayley graph of the modular group are derived by solving the spectral problem on a weighted line that the graph covers.