{"paper":{"title":"Average divisibility in character tables of $\\mathrm{GL}_2(\\mathbb{F}_q)$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.RT","authors_text":"Anwesh Ray, Mishty Ray","submitted_at":"2026-06-26T13:47:45Z","abstract_excerpt":"Let $q$ range over odd prime powers and let $G_q=\\mathrm{GL}_2(\\mathbb{F}_q)$. Fix a prime number $\\ell$. Motivated by work of Peluse and Soundararajan on Miller's conjecture for character tables of symmetric groups, we study the proportion of entries in the character table of $G_q$ which are not divisible by $\\ell$, in the sense of divisibility in the ring of algebraic integers. We prove that $N_\\ell(q)=\\frac{q^4}{2}+O_\\epsilon(q^{3+\\epsilon})$ for every $\\epsilon>0$, where $N_\\ell(q)$ denotes the number of entries which are not divisible by $\\ell$. We also show that the number of zero entrie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28085","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/2606.28085/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"}