Pointwise improvement of the error term in the higher rank hyperbolic lattice counting problem
Dimitrios Chatzakos, Panagiotis Dimakis, Christos Katsivelos
Abstract
We prove an upper bound for the error term in the higher rank hyperbolic lattice counting problem for SL(n, Z). Blomer and Lutsko achieved recently a significant improvement of previous known results by Duke--Rudnick--Sarnak and Gorodnik--Nevo--Yehoshua. We deduce an improved upper bound for the error which holds for almost all pairs z,w ∈ SL(n, R). We also derive a Ω-result for the error term, in the spirit of Rudnick--Phillips.
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