Cubic and quintic analogues of Ramanujan's septic theta function identity
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908388171972608 |
|---|---|
| author | Berndt, Bruce C. Rebák, Örs |
| author_facet | Berndt, Bruce C. Rebák, Örs |
| contents | On page 206 in his lost notebook, Ramanujan recorded an incomplete septic theta function identity. Motivated by the completion of this identity by the second author, we offer cubic and quintic analogues. Using the theory generated by these two analogues and Ramanujan's class invariants, we provide many evaluations for Ramanujan's most prominent theta function, $φ(q)$ in his notation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15513 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cubic and quintic analogues of Ramanujan's septic theta function identity Berndt, Bruce C. Rebák, Örs Number Theory Classical Analysis and ODEs 11F27, 05A30 On page 206 in his lost notebook, Ramanujan recorded an incomplete septic theta function identity. Motivated by the completion of this identity by the second author, we offer cubic and quintic analogues. Using the theory generated by these two analogues and Ramanujan's class invariants, we provide many evaluations for Ramanujan's most prominent theta function, $φ(q)$ in his notation. |
| title | Cubic and quintic analogues of Ramanujan's septic theta function identity |
| topic | Number Theory Classical Analysis and ODEs 11F27, 05A30 |
| url | https://arxiv.org/abs/2312.15513 |