Joint equidistribution of newforms
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_ | 1866911133065019392 |
|---|---|
| author | Nordentoft, Asbjørn Christian Toma, Radu |
| author_facet | Nordentoft, Asbjørn Christian Toma, Radu |
| contents | Let $Y_1$ be a compact arithmetic hyperbolic surface associated to a maximal quaternion order, let $Y_q$ be a cover associated to an Eichler suborder of prime level $q$, and let $ι_q$ be embedding of $Y_q$ as the Hecke correspondence into $Y_1 \times Y_1$. Let $μ_1$ and $μ_q$ be the invariant probability measures on $Y_1$ and $Y_q$, respectively. If $F$ is a newform on $Y_q$, we conjecture that the pushforward measure $(ι_q)_\ast(\lvert F \rvert^2 μ_q)$ converges weakly to the uniform measure $μ_1 \times μ_1$, as $q$ tends to infinity. We prove this conjecture with an effective rate of equidistribution, assuming GRH. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Joint equidistribution of newforms Nordentoft, Asbjørn Christian Toma, Radu Number Theory 11F12 (primary), 11F66 Let $Y_1$ be a compact arithmetic hyperbolic surface associated to a maximal quaternion order, let $Y_q$ be a cover associated to an Eichler suborder of prime level $q$, and let $ι_q$ be embedding of $Y_q$ as the Hecke correspondence into $Y_1 \times Y_1$. Let $μ_1$ and $μ_q$ be the invariant probability measures on $Y_1$ and $Y_q$, respectively. If $F$ is a newform on $Y_q$, we conjecture that the pushforward measure $(ι_q)_\ast(\lvert F \rvert^2 μ_q)$ converges weakly to the uniform measure $μ_1 \times μ_1$, as $q$ tends to infinity. We prove this conjecture with an effective rate of equidistribution, assuming GRH. |
| title | Joint equidistribution of newforms |
| topic | Number Theory 11F12 (primary), 11F66 |
| url | https://arxiv.org/abs/2509.01602 |