Lambda-invariants of Mazur--Tate elements attached to Ramanujan's tau function and congruences with Eisenstein series
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914794730160128 |
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| author | Doyon, Anthony Lei, Antonio |
| author_facet | Doyon, Anthony Lei, Antonio |
| contents | Let $p\in\{3,5,7\}$ and let $Δ$ denote the weight twelve modular form arising from Ramanujan's tau function. We show that $Δ$ is congruent to an Eisenstein series $E_{k,χ, ψ}$ modulo $p$ for explicit choices of $k$ and Dirichlet characters $χ$ and $ψ$. We then prove formulae describing the Iwasawa invariants of the Mazur--Tate elements attached to $Δ$, confirming numerical data gathered by the authors in a previous work. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2209_01669 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lambda-invariants of Mazur--Tate elements attached to Ramanujan's tau function and congruences with Eisenstein series Doyon, Anthony Lei, Antonio Number Theory 11R23 (Primary) 11S40, 11G05 (Secondary) Let $p\in\{3,5,7\}$ and let $Δ$ denote the weight twelve modular form arising from Ramanujan's tau function. We show that $Δ$ is congruent to an Eisenstein series $E_{k,χ, ψ}$ modulo $p$ for explicit choices of $k$ and Dirichlet characters $χ$ and $ψ$. We then prove formulae describing the Iwasawa invariants of the Mazur--Tate elements attached to $Δ$, confirming numerical data gathered by the authors in a previous work. |
| title | Lambda-invariants of Mazur--Tate elements attached to Ramanujan's tau function and congruences with Eisenstein series |
| topic | Number Theory 11R23 (Primary) 11S40, 11G05 (Secondary) |
| url | https://arxiv.org/abs/2209.01669 |