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Combinatorics of the Heat Trace on Spheres

Published online by Cambridge University Press:  20 November 2018

Iosif Polterovich
Iosif Polterovich*
Affiliation:
Institut des Sciences Mathématiques, Université du Québec à Montréal, and Centre de Recherches Mathématiques, Université de Montréal, Montreál, Québec, email: iossif@math.uqam.ca
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Abstract

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We present a concise explicit expression for the heat trace coefficients of spheres. Our formulas yield certain combinatorial identities which are proved following ideas of D. Zeilberger. In particular, these identities allow to recover in a surprising way some known formulas for the heat trace asymptotics. Our approach is based on a method for computation of heat invariants developed in $\left[ \text{P} \right]$.

Keywords

05A1958J35
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 5 , 01 October 2002 , pp. 1086 - 1099
Copyright
Copyright © Canadian Mathematical Society 2002

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