Equivariant heat asymptotics on spaces of automorphic forms
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- by Octavio Paniagua-Taboada and Pablo Ramacher PDF
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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.References
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Additional Information
- Octavio Paniagua-Taboada
- Affiliation: Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans- Meerwein-Strasse 1, 35032 Marburg, Germany
- Email: paniagua@mathematik.uni-marburg.de
- Pablo Ramacher
- Affiliation: Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans- Meerwein-Strasse 1, 35032 Marburg, Germany
- Email: ramacher@mathematik.uni-marburg.de
- Received by editor(s): March 24, 2012
- Received by editor(s) in revised form: October 27, 2013, February 1, 2014, and March 30, 2014
- Published electronically: June 3, 2015
- Additional Notes: The authors wish to thank Roberto Miatello for his encouragement and many stimulating conversations. This work was financed by the DFG-grant RA 1370/2-1.
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 3509-3537
- MSC (2010): Primary 22E46, 53C35, 11F12, 58J40, 58J37, 58J35
- DOI: https://doi.org/10.1090/tran/6439
- MathSciNet review: 3451884