New proofs of two identities of Ramanujan
Fuente:
arXiv
Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910294392963072 |
|---|---|
| author | Morton, Patrick |
| author_facet | Morton, Patrick |
| contents | A proof of several identities of Ramanujan involving theta functions of level $7$ is given which uses a specific modular function for $Γ_1(7)$ and Klein's projective representation of $PSL(2,7)$ into $PSL(3, \mathbb{C})$. Four identities of Berndt and Zhang are derived as algebraic corollaries of the main proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_18140 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New proofs of two identities of Ramanujan Morton, Patrick Number Theory A proof of several identities of Ramanujan involving theta functions of level $7$ is given which uses a specific modular function for $Γ_1(7)$ and Klein's projective representation of $PSL(2,7)$ into $PSL(3, \mathbb{C})$. Four identities of Berndt and Zhang are derived as algebraic corollaries of the main proof. |
| title | New proofs of two identities of Ramanujan |
| topic | Number Theory |
| url | https://arxiv.org/abs/2303.18140 |