The Fourier coefficients and singular moduli of the elliptic modular function $j(τ)$, revisited
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909710361296896 |
|---|---|
| author | Matsusaka, Toshiki |
| author_facet | Matsusaka, Toshiki |
| contents | Kaneko's formula expresses the Fourier coefficients of the elliptic modular $j$-function as finite sums of singular moduli. First published as a short article in 1996, it was presented as a consequence of Zagier's work inspired by Borcherds products. Since then, the formula has developed into a broader framework that links the Fourier coefficients of modular forms to the special values of modular functions, extending in various directions. This article surveys these subsequent developments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Fourier coefficients and singular moduli of the elliptic modular function $j(τ)$, revisited Matsusaka, Toshiki Number Theory 11F30, 11F37, 11F50 Kaneko's formula expresses the Fourier coefficients of the elliptic modular $j$-function as finite sums of singular moduli. First published as a short article in 1996, it was presented as a consequence of Zagier's work inspired by Borcherds products. Since then, the formula has developed into a broader framework that links the Fourier coefficients of modular forms to the special values of modular functions, extending in various directions. This article surveys these subsequent developments. |
| title | The Fourier coefficients and singular moduli of the elliptic modular function $j(τ)$, revisited |
| topic | Number Theory 11F30, 11F37, 11F50 |
| url | https://arxiv.org/abs/2507.21514 |