Local average in the Hyperbolic sphere problem
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911421504159744 |
|---|---|
| author | Cherubini, Giacomo Katsivelos, Christos |
| author_facet | Cherubini, Giacomo Katsivelos, Christos |
| contents | We consider a local average in the hyperbolic lattice point counting problem for the Picard group $Γ$ acting on the three-dimensional hyperbolic space. Compared to the pointwise case, we improve the bounds on the remainder in the counting, conditionally on a quantum variance estimate for Maass cusp forms attached to $Γ$. We also use bounds on a spectral exponential sum over the Laplace eigenvalues for $Γ$, which has been studied in the context of the prime geodesic theorem and for which unconditional bounds are known. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local average in the Hyperbolic sphere problem Cherubini, Giacomo Katsivelos, Christos Number Theory We consider a local average in the hyperbolic lattice point counting problem for the Picard group $Γ$ acting on the three-dimensional hyperbolic space. Compared to the pointwise case, we improve the bounds on the remainder in the counting, conditionally on a quantum variance estimate for Maass cusp forms attached to $Γ$. We also use bounds on a spectral exponential sum over the Laplace eigenvalues for $Γ$, which has been studied in the context of the prime geodesic theorem and for which unconditional bounds are known. |
| title | Local average in the Hyperbolic sphere problem |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.20455 |