|
|||||
|
|
On the Critical Line of Convex Co-Compact Hyperbolic Surfaces |
|
| Authors: | Dmitry Jakobson Frédéric Naud |
| Institution: | 1. Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada, H3A2K6, USA 2. Laboratoire d??Analyse non-lin??aire et G??om??trie, Universit?? d??Avignon et des pays de Vaucluse, F-84018, Avignon, France 3. Centre de Physique Th??orique, Universit?? de Provence Aix-Marseille 1, Campus de Luminy, case 907, 13288, Marseille cedex 09, France |
| Abstract: | Let ?? be a convex co-compact Fuchsian group. We formulate a conjecture on the critical line, i.e. what is the largest half-plane with finitely many resonances for the Laplace operator on the infinite-area hyperbolic surface ${X = \Gamma \backslash \mathbb{H}^2}$ . An upper bound depending on the dimension ?? of the limit set is proved which is in favor of the conjecture for small values of ?? and in the case when ???> 1/2 and ?? is a subgroup of an arithmetic group. New omega lower bounds for the error term in the hyperbolic lattice point counting problem are derived. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |