{"paper":{"title":"On the Atkin $U_t$-operator for $\\Gamma_1(t)$-invariant Drinfeld cusp forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrea Bandini, Maria Valentino","submitted_at":"2017-10-03T09:04:40Z","abstract_excerpt":"We study the diagonalizability of the Atkin $U_t$-operator acting on Drinfeld cusp forms for $\\Gamma_1(t)$ and $\\Gamma(t)$ using Teitelbaum's interpretation as harmonic cocycles. For small weights $k\\leqslant 2q$, we prove $U_t$ is diagonalizable in odd characteristic and we point out that non diagonalizability in even characteristic depends on antidiagonal blocks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01036","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"}