{"paper":{"title":"Banded quadratic digit functions along irreducible polynomials over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kaimin Cheng","submitted_at":"2026-05-25T14:04:47Z","abstract_excerpt":"Let $q$ be an odd prime power and let $\\F_q$ be the finite field with $q$ elements. Let $\\mathcal{P}(n)$ be the set of monic irreducible polynomials of degree $n$ over $\\mathbb{F}_q$. For $f=t^n+f_{n-1}t^{n-1}+\\cdots+f_0\\in\\mathcal{P}(n)$, fix coefficients $c_0,\\ldots,c_m\\in\\mathbb{F}_q$ with $c_m\\ne0$ and put $$ Q_A(f)=\\sum_{j=0}^m c_j\\sum_{i=j}^n f_i f_{i-j}+\\ell_n(f),$$ where $\\ell_n$ is an arbitrary linear form in the coefficients of $f$ and $f_n=1$. We prove that $Q_A$ is equidistributed on $\\mathcal{P}(n)$: for every $\\gamma\\in\\mathbb{F}_q$, $$\\#\\{f\\in\\mathcal{P}(n):Q_A(f)=\\gamma\\}=\\frac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25877","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/2605.25877/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"}