ON THE EXISTENCE OF MAASS CUSP FORMS ON HYPERBOLIC SURFACES WITH CONE POINTS
成果类型：
Article
署名作者：
JUDGE, CM
署名单位：
Institute for Advanced Study - USA
刊物名称：
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN/ISSBN：
0894-0347
DOI：
10.2307/2152928
发表日期：
1995
页码：
715-759
关键词：
摘要：
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 H-2 and a lower bound of 1/2 pi(2) for the eigenvalues of 'odd' Maass cusp forms associated to Hecke triangle groups.
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