Geodesic
On the existence of Maass cusp forms on hyperbolic surfaces with cone points
Journal of the American Mathematical Society, Tome 08 (1995) no. 3, pp. 715-759

Voir la notice de l'article provenant de la source American Mathematical Society

The perturbation theory of the Laplace spectrum of hyperbolic surfaces with conical singularities belonging to a fixed conformal class is developed. As an application, it is shown that the generic such surface with cusps has no Maass cusp forms (${L^2}$ eigenfunctions) under specific eigenvalue multiplicity assumptions. It is also shown that eigenvalues depend monotonically on the cone angles. From this, one obtains Neumann eigenvalue monotonicity for geodesic triangles in ${{\mathbf {H}}^2}$ and a lower bound of $\frac {1}{2}{\pi ^2}$ for the eigenvalues of ‘odd’ Maass cusp forms associated to Hecke triangle groups. 
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Judge, Christopher M. On the existence of Maass cusp forms on hyperbolic surfaces with cone points. Journal of the American Mathematical Society, Tome 08 (1995) no. 3, pp. 715-759. doi: 10.1090/S0894-0347-1995-1273415-6

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