Ninth degree analogue of Ramanujan's septic theta function identity
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910980046323712 |
|---|---|
| author | Kim, Sun Rebák, Örs |
| author_facet | Kim, Sun Rebák, Örs |
| contents | On page 206 in his lost notebook, Ramanujan recorded a seventh degree identity for his theta function $φ(q)$. We give an analogous ninth degree identity. We also provide an application of an entry from his second notebook on a cubic equation and an interpretation with theta functions for some of his trigonometric identities. Lastly, we calculate five examples for $φ(e^{-π\sqrt{n}})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ninth degree analogue of Ramanujan's septic theta function identity Kim, Sun Rebák, Örs Number Theory Classical Analysis and ODEs 33C05, 05A30, 11F32, 11R29 On page 206 in his lost notebook, Ramanujan recorded a seventh degree identity for his theta function $φ(q)$. We give an analogous ninth degree identity. We also provide an application of an entry from his second notebook on a cubic equation and an interpretation with theta functions for some of his trigonometric identities. Lastly, we calculate five examples for $φ(e^{-π\sqrt{n}})$. |
| title | Ninth degree analogue of Ramanujan's septic theta function identity |
| topic | Number Theory Classical Analysis and ODEs 33C05, 05A30, 11F32, 11R29 |
| url | https://arxiv.org/abs/2506.01181 |