Abderemane Morame, Francoise Truc
Eigenvalues of Laplacian with constant magnetic field on noncompact hyperbolic surfaces with finite area
(199K, pdf)

ABSTRACT.  We consider a magnetic Laplacian 
 $-\Delta_A=(id+A)^\star (id+A)$ 
 on a noncompact hyperbolic surface M 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.