Pointwise improvement of the error term in the higher rank hyperbolic lattice counting problem
Year: 2026
Type: preprint
Abstract: We prove an upper bound for the error term in the higher rank hyperbolic lattice counting problem for ${\hbox{SL}(n, \mathbb{Z})}$. 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 $z,w \in {\hbox{SL}(n, \mathbb{R})}$. We also derive a $Ω$-result for the error term, in the spirit of Phillips--Rudnick.
Source: arXiv (Cornell University)
Institutions: University of Patras, University of Maryland, College Park
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221827264