{"paper":{"title":"A primitive normal pair with prescribed prenorm","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"K. Chatterjee, S.K. Tiwari","submitted_at":"2024-06-05T18:35:41Z","abstract_excerpt":"For any positive integers $q$, $n$, $m$ with $q$ being a prime power and $n \\geq 5$, we establish a condition sufficient to ensure the existence of a primitive normal pair $(\\epsilon,f(\\epsilon))$ in $\\mathbb{F}_{q^{n}}$ over $\\mathbb{F}_{q}$ such that $\\mathrm{PN}_{q^n/q}(\\epsilon)=a$, where $a\\in\\mathbb{F}_{q}$ is prescribed. Here $f={f_{1}}/{f_{2}}\\in\\mathbb{F}_{q^n}(x)$ is a rational function subject to some minor restrictions such that deg($f_{1}$)+deg($f_{2}$)$=m$ and $\\mathrm{PN}_{q^n/q}(\\epsilon)\n  =\\sum_{i=0}^{n-1}\\Bigg(\\underset{j\\neq i}{\\underset{0\\leq j\\leq n-1}{\\prod_{}^{}}}\\epsil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03571","kind":"arxiv","version":2},"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/2406.03571/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"}