{"paper":{"title":"Filtrations of dc-weak eigenforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nadim Rustom","submitted_at":"2016-03-09T13:39:23Z","abstract_excerpt":"The notions of strong, weak and dc-weak eigenforms mod $p^n$ was introduced and studied by Chen, Kiming and Wiese. In this work, we prove that there can be no uniform weight bound (that is, depending only on $p$, $n$) on dc-weak eigenforms mod $p^n$ of fixed level when $n \\geq 2$. This is in contrast with the result of Kiming, Rustom and Wiese which establishes a uniform weight bound on strong eigenforms mod $p^n$. As a step towards studying weights bounds for weak eigenforms mod $p^n$, we provide a criterion which allows us to detect whether a given dc-weak eigenform mod $p^n$ is weak."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02884","kind":"arxiv","version":4},"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"}