{"paper":{"title":"Computing an order complete basis for $M^{\\infty}(N)$ and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cristian-Silviu Radu, Mark van Hoeij","submitted_at":"2019-07-01T20:20:06Z","abstract_excerpt":"This paper gives a quick way to construct all modular functions for the group $\\Gamma_0(N)$ having only a pole at $\\tau = i \\infty$. We assume that we are given two modular functions $f,g$ for $\\Gamma_0(N)$ with poles only at $i \\infty$ and coprime pole orders. As an application we obtain two new identities from which one can derive that $p(11n+6)\\equiv 0\\pmod{11}$, here $p(n)$ is the usual partition function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01057","kind":"arxiv","version":1},"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"}