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Transactions of the American Mathematical Society

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Equivariant heat asymptotics on spaces of automorphic forms


Authors: Octavio Paniagua-Taboada and Pablo Ramacher
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
Published electronically: June 3, 2015
MathSciNet review: 3451884
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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.


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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

DOI: https://doi.org/10.1090/tran/6439
Keywords: Equivariant singular asymptotics, heat trace, pseudodifferential operators, locally symmetric spaces
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.
Article copyright: © Copyright 2015 American Mathematical Society

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