Hyperbolic lattice point counting in unbounded rank

We use spectral analysis to give an asymptotic formula for the number of matrices in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>SL</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>n</m:mi> <m:mo>,</m:mo> <m:mi mathvariant="double-struck">Z</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> SL(n,Z) of height at most 𝑇 with strong error terms, far beyond the previous known, both for small and large rank.