{"paper":{"title":"An explicit approach to the Ahlgren-Ono conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Geoffrey D. Smith, Lynnelle Ye","submitted_at":"2014-07-27T21:23:08Z","abstract_excerpt":"Let $p(n)$ be the partition function. Ahlgren and Ono conjectured that every arithmetic progression contains infinitely many integers $N$ for which $p(N)$ is not congruent to $0\\pmod{3}$. Radu proved this conjecture in 2010 using work of Deligne and Rapoport. In this note, we give a simpler proof of Ahlgren and Ono's conjecture in the special case where the modulus of the arithmetic progression is a power of $3$ by applying a method of Boylan and Ono and using work of Bella\\\"iche and Khare generalizing Serre's results on the local nilpotency of the Hecke algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7285","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"}