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| Format: | Preprint |
| Published: |
2023
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| Online Access: | https://arxiv.org/abs/2307.15206 |
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| _version_ | 1866909168482385920 |
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| author | Kobayashi, Masato |
| author_facet | Kobayashi, Masato |
| contents | Ramanujan (1916) and Shen (1999) discovered differential equations for classical Eisenstein series. Motivated by them, we derive new differential equations for Eisenstein series of level 2 from the second kind of Jacobi theta function. This gives a new characterization of a system of differential equations by Ablowitz-Chakravarty-Hahn (2006), Hahn (2008), Kaneko-Koike (2003), Maier (2011) and Toh (2011). As application, we show some arithmetic results on Ramanujan's tau function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15206 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ramanujan-Shen's differential equations for Eisenstein series of level 2 Kobayashi, Masato Number Theory 2020 Primary:11M36, Secondary:11F11 Ramanujan (1916) and Shen (1999) discovered differential equations for classical Eisenstein series. Motivated by them, we derive new differential equations for Eisenstein series of level 2 from the second kind of Jacobi theta function. This gives a new characterization of a system of differential equations by Ablowitz-Chakravarty-Hahn (2006), Hahn (2008), Kaneko-Koike (2003), Maier (2011) and Toh (2011). As application, we show some arithmetic results on Ramanujan's tau function. |
| title | Ramanujan-Shen's differential equations for Eisenstein series of level 2 |
| topic | Number Theory 2020 Primary:11M36, Secondary:11F11 |
| url | https://arxiv.org/abs/2307.15206 |