Equivariant heat asymptotics on spaces of automorphic forms (Q2790598)

Given a connected, real semisimple Lie group \(G\) with finite center, let \(K\) be a compact subgroup of \(G.\) The authors obtain \(K\)-equivariant asymptotics for heat traces with remainder estimates on compact Riemannian manifolds carrying a transitive \(G\)-action. In particular, in the case of the maximal compact subgroup \(K\), the leading coefficients are recovered in the Minakshisundaram-Pleijel expansion [\textit{S. Minakshisundaram} and \textit{Å. Pleijel}, Can. J. Math. 1, 242--256 (1949; Zbl 0041.42701)] of the \(K\)-equivariant heat trace of the Laplace-Beltrami operator on spaces of automorphic forms for arbitrary rank.