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PreprintCC BY 4.0arXiv

Pointwise improvement of the error term in the higher rank hyperbolic lattice counting problem

  • Dimitrios Chatzakos
  • Panagiotis Dimakis
  • Christos Katsivelos
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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 Phillips--Rudnick.

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Cite

BibTeXRIS
BibTeX
@misc{chatzakos2026pointwise,
  title = {{Pointwise improvement of the error term in the higher rank hyperbolic lattice counting problem}},
  author = {Dimitrios Chatzakos and Panagiotis Dimakis and Christos Katsivelos},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16668},
  eprint = {2610.16668},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16668},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Pointwise improvement of the error term in the higher rank hyperbolic lattice counting problem
AU  - Dimitrios Chatzakos
AU  - Panagiotis Dimakis
AU  - Christos Katsivelos
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.16668
UR  - https://arxiv.org/abs/2610.16668
AB  - 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 Phillips--Rudnick.
ER  -