{"paper":{"title":"Stability of Certain Higher Degree Polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Himanshu Sharma, Ritumoni Sarma, Shanta Laishram","submitted_at":"2022-06-09T05:44:26Z","abstract_excerpt":"One of the interesting problems in arithmetic dynamics is to study the stability of polynomials over a field. In this paper, we study the stability of $f(z)=z^d+\\frac{1}{c}$ for $d\\geq 2$, $c\\in{\\mathbb{Z}\\setminus\\{0\\}}$. We show that for infinite families of $d\\geq 3$, whenever $f(z)$ is irreducible, all its iterates are irreducible, that is, $f(z)$ is stable. For $c\\equiv 1\\pmod{4}$, we show that all the iterates of $z^2+\\frac{1}{c}$ are irreducible. Also we show that for $d=3$, if $f(z)$ is reducible, then the number of irreducible factors of each iterate of $f(z)$ is exactly $2$ for $|c|\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.04290","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/2206.04290/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}