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

2022/09/04 by Anthony Doyon, Antonio Lei, Doyon, Anthony +1 · 1 citation
Mathematics · #11G05 (Secondary) #11R23 (Primary) 11S40 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2209.01669

openalex publication_date 2022/09/04 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

Let p∈\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.

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• On the maximality of the λ-invariants of Mazur--Tate elements

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