{"paper":{"title":"On some constancy of Hecke eigensystems for Drinfeld cuspforms of level $\\Gamma_1(\\mathfrak{n}\\wp^r)$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shin Hattori","submitted_at":"2026-05-18T08:07:32Z","abstract_excerpt":"Let $p$ be a rational prime, let $q>1$ be a $p$-power integer, let $\\mathbb{F}_q$ be the field of $q$ elements and let $A=\\mathbb{F}_q[t]$ be the polynomial ring over $\\mathbb{F}_q$. Let $\\mathfrak{n}\\in A$ be a nonzero element and let $\\wp\\in A$ be a monic irreducible polynomial of positive degree. Let $k\\geq 2$ and $r\\geq 1$ be integers. Let $S_k(\\Gamma_1(\\mathfrak{n}\\wp^r))$ be the space of Drinfeld cuspforms of level $\\Gamma_1(\\mathfrak{n}\\wp^r)$ and weight $k$. In this paper, we show that a Hecke eigensystem of finite $\\wp$-slope appears in $S_k(\\Gamma_1(\\mathfrak{n}\\wp^r))$ if and only i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18016","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18016/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.524559Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"64230f339c33b05e4242d3ba76e9508f073175008bff4a918de3c28abb82ce68"},"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"}