Arithmetic constants for symplectic variances of the divisor function
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912106681466880 |
|---|---|
| author | Kuperberg, Vivian Lalín, Matilde |
| author_facet | Kuperberg, Vivian Lalín, Matilde |
| contents | In [arXiv:2212.04969], the authors stated some conjectures on the variance of certain sums of the divisor function $d_k(n)$ over number fields, which were inspired by analogous results over function fields proven in [arXiv:2107.01437]. These problems are related to certain symplectic matrix integrals. While the function field results can be directly related to the random matrix integrals, the connection between the random matrix integrals and the number field results is less direct and involves arithmetic factors. The goal of this article is to give heuristic arguments for the formulas of these arithmetic factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arithmetic constants for symplectic variances of the divisor function Kuperberg, Vivian Lalín, Matilde Number Theory 11N60 (Primary), 05A15, 11M50, 11N56 (Secondary) In [arXiv:2212.04969], the authors stated some conjectures on the variance of certain sums of the divisor function $d_k(n)$ over number fields, which were inspired by analogous results over function fields proven in [arXiv:2107.01437]. These problems are related to certain symplectic matrix integrals. While the function field results can be directly related to the random matrix integrals, the connection between the random matrix integrals and the number field results is less direct and involves arithmetic factors. The goal of this article is to give heuristic arguments for the formulas of these arithmetic factors. |
| title | Arithmetic constants for symplectic variances of the divisor function |
| topic | Number Theory 11N60 (Primary), 05A15, 11M50, 11N56 (Secondary) |
| url | https://arxiv.org/abs/2410.17939 |