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On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$
In this paper, we obtain an explicit formula for the heat kernel on the Cayley graph of the modular group $PSL_2(Z)$, given by the presentation $\langle a,b\mid a^2=1, b^3=1\rangle$. Our approach extends a method of Chung--Yau by observing that the Cayley graph strongly and regularly covers a weight
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