Combinatorics/Geometry
Harmonic-counting measures and spectral theory of lens spaces
Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1145-1150.

In this article, associated with each lattice TZn, the concept of a harmonic-counting measure νT on a sphere Sn1 is introduced and is applied to determine the asymptotic behavior of the cardinality of the set of independent eigenfunctions of the Laplace–Beltrami operator on a lens space L corresponding to the elements of the associated lattice T of L lying in a cone.

Dans cette Note, on associe à tout réseau TZn une mesure de comptage harmonique νT sur la sphère Sn1. On l'utilise pour déterminer le comportement asymptotique du cardinal d'un ensemble de fonctions propres indépendantes de l'opérateur de Laplace–Beltrami sur un espace lenticulaire L, correspondant aux éléments du réseau T de L appartenant à un cône.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.10.016
Mohades, Hossein 1; Honari, Bijan 1

1 Faculty of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., 15914, Tehran, Iran
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Mohades, Hossein; Honari, Bijan. Harmonic-counting measures and spectral theory of lens spaces. Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1145-1150. doi : 10.1016/j.crma.2016.10.016. http://www.numdam.org/articles/10.1016/j.crma.2016.10.016/

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