Lacunary recurrences and 2-adic properties of Eisenstein series
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910207474401280 |
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| author | Chiriac, Liubomir Jorza, Andrei |
| author_facet | Chiriac, Liubomir Jorza, Andrei |
| contents | We study the rational coefficients that arise when the Eisenstein series $G_k$ is expressed as a polynomial in $G_4$ and $G_6$. We prove a recent conjecture giving an exact formula for the minimal 2-adic valuation of these coefficients in terms of the binary expansion of the weight. The proof uses lacunary recurrences for Eisenstein series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09738 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lacunary recurrences and 2-adic properties of Eisenstein series Chiriac, Liubomir Jorza, Andrei Number Theory We study the rational coefficients that arise when the Eisenstein series $G_k$ is expressed as a polynomial in $G_4$ and $G_6$. We prove a recent conjecture giving an exact formula for the minimal 2-adic valuation of these coefficients in terms of the binary expansion of the weight. The proof uses lacunary recurrences for Eisenstein series. |
| title | Lacunary recurrences and 2-adic properties of Eisenstein series |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.09738 |