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arXiv · 2209.01669

Lambda-invariants of Mazur--Tate elements attached to Ramanujan's tau function and congruences with Eisenstein series

Anthony Doyon·Antonio Lei
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Abstract

Let $p\in\{3,5,7\}$ and let $\Delta$ denote the weight twelve modular form arising from Ramanujan's tau function. We show that $\Delta$ is congruent to an Eisenstein series $E_{k,\chi, \psi}$ modulo $p$ for explicit choices of $k$ and Dirichlet characters $\chi$ and $\psi$. We then prove formulae describing the Iwasawa invariants of the Mazur--Tate elements attached to $\Delta$, confirming numerical data gathered by the authors in a previous work.

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Anthony Doyon, Antonio Lei. 2022-09-04. Lambda-invariants of Mazur--Tate elements attached to Ramanujan's tau function and congruences with Eisenstein series. https://arxiv.org/abs/2209.01669

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