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We study the asymptotic distribution of the resonances near the Landau levels$\Lambda\_q =(2q+1)b$, $q \in \mathbb{N}$, of the Dirichlet (resp. Neumann,resp. Robin) realization in the exterior of a compact domain of $\mathbb{R}^3$of the 3D Schr{\"o}dinger operator with constant magnetic field of scalarintensity $b\textgreater{}0$. We investigate the corresponding resonancecounting function and obtain the main asymptotic term. In particular, we provethe accumulation of resonances at the Landau levels and the existence ofresonance free sectors. In some cases, it provides the discreteness of the setof embedded eigenvalues near the Landau levels.

Counting function of magnetic resonances for exterior problems