Geodesic
Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds
Journal of the European Mathematical Society, Tome 18 (2016) no. 5, pp. 997-1041.

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On geometrically finite hyperbolic manifolds Γ\Hd, including those with non-maximal rank cusps, we give upper bounds on the number N(R) of resonances of the Laplacian in disks of size R as R→∞. In particular, if the parabolic subgroups of Γ satisfy a certain Diophantine condition, the bound is N(R)=O(Rd(logR)d+1).
DOI : 10.4171/jems/607
Classification : 58-XX, 35-XX
Keywords: Spectral geometry, hyperbolic manifolds, resonances 
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     author = {David Borthwick and Colin Guillarmou},
     title = {Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds},
     journal = {Journal of the European Mathematical Society},
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David Borthwick; Colin Guillarmou. Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds. Journal of the European Mathematical Society, Tome 18 (2016) no. 5, pp. 997-1041. doi : 10.4171/jems/607. http://geodesic.mathdoc.fr/articles/10.4171/jems/607/

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