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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.17753 |
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Table of Contents:
- For $n\geq 3$ and $Γ$ a cocompact lattice acting on the hyperbolic space $\mathbb{H}^n$, we investigate the average behaviour of the error term in the circle problem. First, we explore the local average of the error term over compact sets of $Γ\backslash\mathbb{H}^n$. Our upper bound depends on the quantum variance and the spectral exponential sums appearing in the study of the Prime geodesic theorem. We also prove $Ω$-results for the mean value and the second moment of the error term.