论文标题
Mazur-tate元素的Lambda-invariants附加了Ramanujan的tau功能和与Eisenstein系列的一致性
Lambda-invariants of Mazur--Tate elements attached to Ramanujan's tau function and congruences with Eisenstein series
论文作者
论文摘要
令$ p \ in \ {3,5,7 \} $，让$δ$表示由Ramanujan的Tau功能引起的重量十二个模块化形式。我们表明，$δ$与Eisenstein系列$ e_ {k，χ，ψ} $ modulo $ p $一致，以明确选择$ k $和dirichlet字符$χ$和$ψ$。然后，我们证明了描述$δ$的Mazur-Tate元素的Iwasawa不变性的公式，这证实了作者在先前的工作中收集的数值数据。
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.
