The $\Theta$ Function and the Weyl Law on Manifolds Without Conjugate Points
Documenta mathematica, Tome 22 (2017), pp. 1275-1283.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove that the usual $\Theta$ function on a Riemannian manifold without conjugate points is uniformly bounded from below. This extends a result of Green in two dimensions. We deduce that the Bérard remainder in the Weyl law is valid for a manifold without conjugate points, without any restriction on the dimension.
Classification : 35P20
Keywords: Weyl law, manifolds without conjugate points, Hadamard parametrix, Jacobi and Ricatti equations
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     author = {Bonthonneau, Yannick},
     title = {The $\Theta$ {Function} and the {Weyl} {Law} on {Manifolds} {Without} {Conjugate} {Points}},
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Bonthonneau, Yannick. The $\Theta$ Function and the Weyl Law on Manifolds Without Conjugate Points. Documenta mathematica, Tome 22 (2017), pp. 1275-1283. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a14/