# Eigenvalues of Laplacian with constant magnetic field on non-compact hyperbolic surfaces with finite area

Abstract : We consider a magnetic Laplacian $-\Delta_A=(id+A)^\star (id+A)$ on a noncompact hyperbolic surface $\mM$ with finite area. $A$ is a real one-form and the magnetic field $dA$ is constant in each cusp. When the harmonic component of $A$ satifies some quantified condition, the spectrum of $-\Delta_A$ is discrete. In this case we prove that the counting function of the eigenvalues of $-\Delta_{A}$ satisfies the classical Weyl formula, even when $dA=0.$
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https://hal.archives-ouvertes.fr/hal-00462411
Contributor : Francoise Truc <>
Submitted on : Monday, May 10, 2010 - 5:26:54 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on : Thursday, September 23, 2010 - 1:07:09 PM

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Abderemane Morame, Francoise Truc. Eigenvalues of Laplacian with constant magnetic field on non-compact hyperbolic surfaces with finite area. Letters in Mathematical Physics, Springer Verlag, 2011, 97 (2), pp.203-211. ⟨10.1007/s11005-011-0489-6⟩. ⟨hal-00462411v2⟩

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