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We consider a compact Riemannian manifold Y without boundary assuming that Y has conic singularities. We obtain an asymptotic of Beltrami operator L on Y. This enables us to obtain the asymptotic of the function N(λ) computing the eigenvalues of L less than λ 2 On considere une variete nemannienne compacte Y sans bord ayant des singularites coniques. On obtient une asymptotique de la fonction spectrale associee a l'operateur de Laplace-Beltrami L sur Y. On en deduit l'asymptotique de la fonction N(λ) comptant des valeurs propres de L plus petites que λ 2

Comportement asymptotique de la fonction spectrale de l'opérateur de Laplace-Beltrami sur une variété ayant des singularités coniques