Equivariant heat asymptotics on spaces of automorphic forms

Paniagua-Taboada, Octavio; Ramacher, Pablo

doi:10.1090/tran/6439

Equivariant heat asymptotics on spaces of automorphic forms
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by Octavio Paniagua-Taboada and Pablo Ramacher PDF

Trans. Amer. Math. Soc. 368 (2016), 3509-3537 Request permission

Abstract:

Let $G$ be a connected, real, semisimple Lie group with finite center and $K$ a compact subgroup of $G$. In this paper, we derive $K$-equivariant asymptotics for heat traces with remainder estimates on compact Riemannian manifolds carrying a transitive $G$-action. In particular, if $K$ is a maximal compact subgroup, we recover the leading coefficient in the Minakshisundaram-Pleijel expansion of the $K$-equivariant heat trace of the Laplace-Beltrami operator on spaces of automorphic forms for arbitrary rank.

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