{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/lambda-invariants-of-mazur-tate-elements","title":"Lambda-invariants of Mazur--Tate elements attached to Ramanujan's tau function and congruences with Eisenstein series","arxiv_id":"2209.01669","date":"2022-09-04","proceeding":null,"authors":["Anthony Doyon","Antonio Lei"],"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.","url_abs":"https://arxiv.org/abs/2209.01669v2","url_pdf":"https://arxiv.org/pdf/2209.01669v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"lambda-invariants-of-mazur-tate-elements","repo_url":"https://github.com/anthonydoyon/Ramanujan-s-tau-and-MT-elts","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}