Comptes Rendus
no. 12
Combinatorics/Geometry
Harmonic-counting measures and spectral theory of lens spaces

Presented by: the Editorial Board

Hossein Mohades1; Bijan Honari1
1 Faculty of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., 15914, Tehran, Iran
Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1145-1150.

In this article, associated with each lattice T⊆Zn, the concept of a harmonic-counting measure νT on a sphere Sn−1 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 T⊆Zn une mesure de comptage harmonique νT sur la sphère Sn−1. 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

Hossein Mohades 1; Bijan Honari 1

1 Faculty of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., 15914, Tehran, Iran 
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Hossein Mohades; Bijan Honari. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.10.016/

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