Abstract
Let be a finite-volume Fuchsian group. The hyperbolic circle problem is the estimation of the number of elements of the -orbit of in a hyperbolic circle around of radius , where and are given points of the upper half plane and is a large number. An estimate with error term is known, and this has not been improved for any group. Recently, Risager and Petridis proved that in the special case taking and averaging over in a certain way the error term can be improved to . Here we show such an improvement for a general ; our error term is (which is better than but weaker than the estimate of Risager and Petridis in the case ). Our main tool is our generalization of the Selberg trace formula proved earlier.
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