Supercongruences arising from Ramanujan-Sato Series
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929756611543040 |
|---|---|
| author | Babei, Angelica Roy, Manami Swisher, Holly Tobin, Bella Tu, Fang-Ting |
| author_facet | Babei, Angelica Roy, Manami Swisher, Holly Tobin, Bella Tu, Fang-Ting |
| contents | Recently, the authors with Lea Beneish established a recipe for constructing Ramanujan-Sato series for $1/π$, and used this to construct 11 explicit examples of Ramanujan-Sato series arising from modular forms for arithmetic triangle groups of non-compact type. Here, we use work of Chisholm, Deines, Long, Nebe and the third author to prove a general $p$-adic supercongruence theorem through an explicit connection to CM hypergeometric elliptic curves that provides $p$-adic analogues of these Ramanujan-Sato series. We further use this theorem to construct explicit examples related to each of our explicit Ramanujan-Sato series examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08844 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Supercongruences arising from Ramanujan-Sato Series Babei, Angelica Roy, Manami Swisher, Holly Tobin, Bella Tu, Fang-Ting Number Theory Recently, the authors with Lea Beneish established a recipe for constructing Ramanujan-Sato series for $1/π$, and used this to construct 11 explicit examples of Ramanujan-Sato series arising from modular forms for arithmetic triangle groups of non-compact type. Here, we use work of Chisholm, Deines, Long, Nebe and the third author to prove a general $p$-adic supercongruence theorem through an explicit connection to CM hypergeometric elliptic curves that provides $p$-adic analogues of these Ramanujan-Sato series. We further use this theorem to construct explicit examples related to each of our explicit Ramanujan-Sato series examples. |
| title | Supercongruences arising from Ramanujan-Sato Series |
| topic | Number Theory |
| url | https://arxiv.org/abs/2408.08844 |