Comptes Rendus
no. 12
Combinatorics/Geometry
Harmonic-counting measures and spectral theory of lens spaces
[Mesures de comptage harmonique et théorie spectrale des espaces lenticulaires]

Présenté par : 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.

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.

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.

Reçu le :
Accepté le :
Publié le :
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/

[1] I. Chavel Eigenvalues in Riemannian Geometry, vol. 115, Academic Press, 1984

[2] P.L. Clark Geometry of numbers with applications to number theory www.math.uga/edu/pete/geometryofnumbers.pdf (Notes available at:)

[3] M. Duchin; S. Lelièvre; C. Mooney The geometry of spheres in free Abelian groups, Geom. Dedic., Volume 161 (2012) no. 1

[4] E. Ehrhart Sur les polyèdres rationnels homothétiques à n dimensions, C. R. Acad. Sci. Paris, Volume 254 (1962), pp. 616-618

[5] A. Ikeda On the spectrum of a Riemannian manifold of positive constant curvature, Osaka J. Math., Volume 17 (1980) no. 1, pp. 75-93

[6] A. Ikeda, Riemannian manifolds p-isospectral but not p+1-isospectral, in: Geometry of Manifolds (Matsumoto, 1988), Perspect. Math., vol. 8, 1989, pp. 383–417.

[7] E.A. Lauret Spectra of orbifolds with cyclic fundamental groups, Ann. Glob. Anal. Geom., Volume 50 (2016), pp. 1-28

[8] E.A. Lauret; R.J. Miatello; J.P. Rossetti Spectra of lens spaces from 1-norm spectra of congruence lattices, Int. Math. Res. Not. IMRN (2016) no. 4, pp. 1054-1089

[9] H. Mohades; B. Honari On a relation between spectral theory of lens spaces and Ehrhart theory, 2016 | arXiv

[10] R.P. Stanley Decompositions of rational convex polytope, Ann. Discrete Math., Volume 6 (1980), pp. 333-342

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