Weighted geodesic restrictions of arithmetic eigenfunctions
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_ | 1866914178358312960 |
|---|---|
| author | Hou, Jiaqi Huang, Xiaoqi |
| author_facet | Hou, Jiaqi Huang, Xiaoqi |
| contents | Let $X$ be an arithmetic hyperbolic surface, $ψ$ a Hecke-Maass form, $\ell$ a geodesic segment on $X$, and $μ$ a Borel measure supported on $\ell$ with dimension greater than 1/2. We obtain a power saving over the local bound of Eswarathasan and Pramanik for the $L^2$ norm of $ψ$ with respect to $μ$, which is a weighted generalization of Marshall's geodesic restriction bound and is proved by applying the method of arithmetic amplification. On a general 2-dimensional Riemannian manifold, we also obtain a Kakeya-Nikodym bound for the $L^2$ norm of any Laplace-Beltrami eigenfunction with respect to a Borel measure supported on a geodesic segment with dimension greater than 1/2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03291 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted geodesic restrictions of arithmetic eigenfunctions Hou, Jiaqi Huang, Xiaoqi Number Theory Analysis of PDEs 58J50, 11F03 Let $X$ be an arithmetic hyperbolic surface, $ψ$ a Hecke-Maass form, $\ell$ a geodesic segment on $X$, and $μ$ a Borel measure supported on $\ell$ with dimension greater than 1/2. We obtain a power saving over the local bound of Eswarathasan and Pramanik for the $L^2$ norm of $ψ$ with respect to $μ$, which is a weighted generalization of Marshall's geodesic restriction bound and is proved by applying the method of arithmetic amplification. On a general 2-dimensional Riemannian manifold, we also obtain a Kakeya-Nikodym bound for the $L^2$ norm of any Laplace-Beltrami eigenfunction with respect to a Borel measure supported on a geodesic segment with dimension greater than 1/2. |
| title | Weighted geodesic restrictions of arithmetic eigenfunctions |
| topic | Number Theory Analysis of PDEs 58J50, 11F03 |
| url | https://arxiv.org/abs/2512.03291 |