{"paper":{"title":"On the algebraic structure of iterated integrals of quasimodular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nils Matthes","submitted_at":"2017-08-15T15:39:48Z","abstract_excerpt":"We study the algebra $\\mathcal{I}^{QM}$ of iterated integrals of quasimodular forms for $\\operatorname{SL}_2(\\mathbb{Z})$, which is the smallest extension of the algebra $QM_{\\ast}$ of quasimodular forms, which is closed under integration. We prove that $\\mathcal{I}^{QM}$ is a polynomial algebra in infinitely many variables, given by Lyndon words on certain monomials in Eisenstein series. We also prove an analogous result for the $M_{\\ast}$-subalgebra $\\mathcal{I}^{M}$ of $\\mathcal{I}^{QM}$ of iterated integrals of modular forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04561","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}